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CS0001
Discrete Structures
| Question | Answer |
|---|---|
| Which algorithm is being used by Facebook to transmit videos quickly on the Internet. | Audio and Video compression algorithm |
| Which of the following is an example of a Discrete Data? Group of answer choices water temperature Wind speed number of students enrolled volts of electricity | number of students enrolled |
| Which of the following is not your job as a Computer Scientist? Group of answer choices Creating new algorithms none of the above Proving that your algorithm works Proving that your algorithms terminate | None of the above |
| Which of the following is not an example of a Continuous Data? Group of answer choices 3 laptops 3.25 kg 7.25 inches 1.32 miles | 3 laptops |
| Math is not important in Discrete Structures. | False |
| Which of the following is not a route finding algorithm? Group of answer choices A* Search Algorithm D* Search Algorithm Dijkstra’s Algorithm O* Search Algorithm | O* Search Algorithm |
| Discrete Data is counted | True |
| Which of the following is an example of a Discrete Data? Group of answer choices Wind speed volts of electricity number of tickets sold water temperature | number of tickets sold |
| Which of the following is an example of a Continuous Data? Group of answer choices Number of students in a university Height No of wins in a season Number of Facebook likes | Height |
| Which of the following is not an example of a Discrete Data? Group of answer choices 1.32 miles 3 laptops 96 workers 5 kids | 1.32 miles |
| Data that involves complex numbers that are measured across a specific time interval. Group of answer choices Continuous data Discrete data | Continuous data |
| Which algorithm is being used by Waze to give you the best route from one place to another? Group of answer choices optimization algorithm scheduling algorithm audio and video compression algorithm route finding algorithm | route finding algorithm |
| Continuous data is measureable | True |
| If you will be counting the total numbers of students inside a classroom, what type of date will you be having? Group of answer choices Continuous data Discrete data | Discrete data |
| Discrete Structures is a foundational material for Computer Science. Group of answer choices True False | True |
| What is the negation of the given proposition? I read books everyday. Group of answer choices I always read books everyday I don't read books everyday none of the above I will read books everyday | I don't read books everyday |
| Which of the rules of replacement states that, ~(p /\ q) = ~p V ~q ~(p V q) = ~p /\ ~q - Double Negation Law - Commutative Law - De Morgan’s Law - Distributive Law | De Morgan's Law |
| A compound proposition that is always ___________ is called a tautology. Group of answer choices True False | True |
| It is a statement that is always false Group of answer choices none of the above Contradiction Contingency Tautology | Contradiction |
| Which of the rules of replacement states that, p ∨ c ≡ p p ∧ t ≡ p - Identity Law - Commutative Law - De Morgan’s Law - none of the above | Identity Law |
| It is a statement that is always true. Group of answer choices Tautology Contingency Contradiction none of the above | Tautology |
| A declarative sentence that is either true or false, but not both. Group of answer choices Statement Contradiction False Tautology | Statement |
| Which of the rules of replacement states that, [p ∨ (q ∨ r)] ≡ [(p ∨ q) ∨ r] [p ∧ (q ∧ r)] ≡ [(p ∧ q) ∧ r] Group of answer choices Associative law Double Negation De Morgan’s Law none of the above | Associative Law |
| Two statements are logically equivalent if they have the same truth table. Group of answer choices True False | True |
| It is a property that some object has. Group of answer choices Predicate Subject Object Proposition | Predicate |
| Is the given expression a proposition? Are you sick? Group of answer choices Yes no | no |
| Which of the rules of replacement states that, [p ∧ (q ∨ r)] ≡ [(p ∧ q) ∨ (p ∧ r)] [p ∨ (q ∧ r)] ≡ [(p ∨ q) ∧ (p ∨ r)] Group of answer choices none of the above De Morgan's Law Distributive Law Commutative Law | Distributive Law |
| Is the given expression a proposition? Feed me. Group of answer choices Yes no | no |
| Is the given expression a proposition? The elephant is pink. Group of answer choices no Yes | Yes |
| s the given expression a proposition? X=x+3 Group of answer choices Yes no | Yes? |
| Which of the following is not an example of Discrete data. Group of answer choices Number of languages an individual speaks. The number of test questions you answered correctly. The speed of cars The number of home runs in a baseball game | The speed of cars |
| Discrete data can take any value in an interval. Group of answer choices True False | False* |
| Which of the following is an example of a Discrete Data? Group of answer choices Wind speed water temperature number of customers who bought different items volts of electricity | number of customers who bought different items |
| Which of the following is not an example of a Discrete Data? Group of answer choices 30.8 °c 5 balls 8 pins 1 student | 30.8 °c |
| Continuous data can only have specific values. Group of answer choices True False | False |
| It is a gateway to more advanced courses in the field of mathematical science. | Discrete Structures |
| Which of the following is an example of a Discrete data. Group of answer choices Time to wake up The speed of cars The weight of a truck Number of languages an individual speaks. | Number of languages an individual speaks |
| Discrete Structures develop Mathematical reasoning. Group of answer choices True False | True |
| Which of the following is an example of a Continuous data. Group of answer choices The height of children. The number of students in a class The number of workers in a company. Instruments in a shelf | The height of children |
| A compound proposition that is always ___________ is called a contradiction. Group of answer choices True False | False |
| A compound proposition that is neither a tautology nor a contradiction is called a ___________ | Contingency |
| Which of the rules of replacement states that, p ≡¬ (¬ p) Group of answer choices none of the above De Morgan’s Law Associative laws Double Negation | Double Negation |
| It is the science of necessary inference or study of reasoning | logic |
| p->(p v q) is a tautology | True |
| is ~p -> p a tautology? | False |
| Is the given expression a proposition? Did you eat your lunch? | No |
| What is the missing statement? 1. (~p v q) -> ~(q /\ r) Premise 2. q /\ r Premise 3. --------------- 1,2 Modus Tollens | p ∨ q ≡ q ∨ p |
| Which rule of inference states that p _________ ∴ p V q | Addition |
| Determine the rules of inference: "The ice cream is not vanilla flavored", "The ice cream is either vanilla flavored or chocolate flavored" Therefore - "The ice cream is chocolate flavored" | Disjunctive Syllogism |
| What is the rule of inference? 1. p -> ~(q/\r) 2. q /\ Premise 3. ~p ---- | 1,2 modus Tollens |
| Determine the rules of inference: If it rains, I shall not go to school if I don't go to school, I won't need to do homework If it rains, I won't need to do homework | Hypothetical Syllogism |
| What is the missing statement? 1. p -> ~q Premise 2. p Premise 3. ----- 1, 2 Modus Ponens | ~q * |
| Determine the rules of inference : “I will study discrete math and English literature” “Therefore, I will study discrete math.” | Simplification |
| Which rule of inference states that, p -> q q ->r ------------ ∴ p -> r | Hypothetical Syllogism |
| Which of the following is a method of proof? Proof by Contradiction Proof by Correction Method of no Return all of the above | Proof by Contradiction |
| Determine the rules of inference : "If you have a password, then you can log on to facebook", "You cannot log on to facebook", Therefore − "You do not have a password " | Modus Tollens |
| Determine the rules of inference : “I will read books and eat cake” “Therefore, I will read books” | Simplification |
| What is the missing statement? 1. ~(~p v q) Premise 2. ---------- De Morgan | p /\ ~q |
| Which rule of inference states that, p -> q ~q ------------- ∴ ~p | Modus Tollens |
| Determine the rules of inference : "If it is snowing, then I will study discrete math.” “It is snowing.” “Therefore , I will study discrete math | Modus Ponens |
| What is the missing rule of inference? 1. 𝑝 → ¬𝑞 (premise) 2. ¬𝑞 → 𝑟 (premise) 3. ¬𝑟 (premise) 4. 𝑝 → 𝑟 (hypothetical syllogism from 1, 2) 5. ∴ ¬𝑝 _____?_______ | modus tollens from 3, 4) |
| Determine the rules of inference : “If it is snowing, then I will study discrete math.” “I will not study discrete math.” “Therefore , it is not snowing.” | Modus Tollens |
| Name this argument form: If P then Q. P. Therefore Q. | Modus Ponens |
| Determine the rules of inference for: The ice cream is vanilla flavored or chocolate flavored The ice cream is not vanilla flavored Therefore The ice cream is chocolate flavored | Disjunctive Syllogism |
| This is the corresponding tautology for Modus Ponens. (p ∧ (p →q)) → q ( ¬ q ∧ (p →q)) → ¬p p ∨ q ≡ q ∨ p No answer text provided. | (p ∧ (p →q)) → q |
| Write each of the following in set builder form. A = {5, 10, 15, 20} | {x : x is a multiple of 5 and 5 ≤ x ≤ 20} |
| Which of the following is an empty (null) set? {tiger, lion, puma, cheetah} {cars with more than 20 doors} {prime numbers between 1 and 100 all of the above | {cars with more than 20 doors} |
| Which of the following is the set of odd whole numbers less than 10? C={0,1,2,3,4,5,6,7,8,9} D={0,2,4,6,8} E={1,3,5,7,9} none of the above | E={1,3,5,7,9} |
| What type of set is H? H={..., -3,-2,-1,0, 1,2,3...} | infinite |
| Jennifer listed the set of all letters in the word library as shown below. What is wrong with this set? A={l,i,b,r,a,r,y} | The objects in this set are not unique |
| B = {1,2,3,4,7} 10 ∉ B [True or False] | True |
| What is the cartesian product of {a,b} X {0,1} | {(a,1), (a,0), (b,1), (b,0)} |
| Is A a subset of B? A = {1,2,11} B = {1,2,3,4,5,6,7} | no |
| Which of the following is the set of all oceans on earth? G={Atlantic, Pacific, Arctic, Indian, Antarctic} E={Amazon, Nile, Mississippi, Rio Grande, Niagara} F={Asia, Africa, North America, South America, Antarctica, Europe, Australia} | G={Atlantic, Pacific, Arctic, Indian, Antarctic} |
| This means “not an element of” | ∉ |
| Let C = {apple, grapes, banana, melon, orange} The cardinality of C is? | 5 |
| Let C = {Maria, Joseph, Mariano} The cardinality of C is? | 3 |
| Which of the following sets are infinite? {vowels} {days of the week} {primary colors} none of the above | none of the above |
| If A = {7, 8} and B = {2, 4, 6}, find A × B. | {(7, 2); (7, 4); (7, 6); (8, 2); (8, 4); (8, 6)} |
| Which of the following is a true statement for set R? R={liquid, gas, solid, plasma} gas ∉ R solid ∉ r liquid ∈ R none of the above | liquid ∈ R |
| It is a measure of a set's size, meaning the number of elements in the set. | Cardinality |
| Which of the following is the set of all suits in a standard deck of playing cards? R={ace, two, three, four, five, king} S={hearts, diamonds, clubs, spades} T={jokers} none of the above | S={hearts, diamonds, clubs, spades} |
| In this method, a set is described by a characterizing property of its element x. | Set-Builder Notation |
| In this method, a set is described by listing elements, separated by commas within braces { }. | Set-Roster Notation |
| Which of the following is not a subset of P? P={c,l,e,a,r} Q={e,a,r} R={r,e,a,l} S={l,e,a,r,n} T={c,a,r,e} | S={l,e,a,r,n} |
| Write each of the following in set builder form. L = {1, 3, 5, 7, 9} | {x : x is odd, x ≤ 9} |
| Determine the rules of inference for: The soul is immortal or it is mortal. The soul is not immortal. Therefore it is mortal. | Disjunctive Syllogism |
| [True or False] Evidences are the premises, they are the assumptions. | True |
| Determine the rules of inference : “He studies very hard” “He is the best boy in the class” Therefore − "He studies very hard and he is the best boy in the class" | Conjunction |
| What is the missing statement? 1. (~p v q) -> ~(q /\ r) Premise 2. ~p v q Premise 3. ------- 1,2 Modus Ponens | ~(q∧ r) |
| Determine the rules of inference : “I will eat ice cream and cake” “Therefore, I will eat ice cream” | Simplification |
| Determine the rules of inference for: If you repent, you will go to heaven. You have repented. So you will go to heaven. | Modus Ponens |
| If A = { 1, 3, 5} and B = {2, 3}, then Find: A × A | [{1, 1},{1, 3},{1, 5},{3, 1},{3, 3},{3, 5},{5, 1},{5, 3},{5, 5}] |
| If A = { 1, 3, 5} and B = {2, 3}, then Find: B × B | [{2, 2},{2, 3},{3, 2},{3, 3}] |
| Write the cardinal number of X = The set of months in a year. | 12 |
| Write the following sets in the roster form: A = The set of all even numbers less than 12 | A={2, 4, 6, 8, 10} |
| Write the cardinal number of Y = The set of letters in the word INTELLIGENT | 6 |
| What is the cardinality of set A? A={2,4,6,8,10} | |A|=5 |
| π (set of irrational numbers) ∉ Z (set of integers) | True |
| The set of positive integers is _____________ | Infinite |
| Find the inverse of each relation. {(4, 15), (8, 18)} {(4, 4), (8, 8)} {(4, 15), (8, 18)} {(18, 15), (8, 4)} none of the above | none of the above |
| Find the inverse of {(4, 3), (–4, –4), (–3, –5), (5, 2)} | {(3, 4), (–4, –4), (–5, –3), (2, 5)} |
| Given the relation below: {(–8, 6), (6, –2), (7, –3)} Find the range of the inverse of the relation. | {6, -2, -3} |
| Given the relation below: {(1, p), (1, r), (4, q), (5, s)} Find the domain of the inverse of the relation. | {p,r,q,s} |
| Find the inverse of {(–8, 6), (6, –2), (7, –3)} | {(6, –8), (–2, 6), (–3, 7)} |
| Given the relation below: {(1, 2), (3, 4), (5, 6), (7, 8)} Find the range of the inverse of the relation. | {1, 3, 5, 7} |
| State the range of the following relation: {(1,3), (-2,7), (3,-3), (4,5), (1,-3)}. | {-3, 3, 5, 7} |
| Given the relation below: {(7, 7), (4, 9), (3, –7)} Find the range of the inverse of the relation. | {7, 4, 3} |
| Find the inverse of {(1, –5), (2, 6), (3, –7), (4, 8), (5, –9)} | {(–5, 1), (6, 2), (–7, 3), (8, 4), (–9, 5)} |
| State the domain of the following relation. {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} | {2, 4, 3, 6,2} |
| Find the inverse of {(0, 3), (4, 5), (–8, 7), (12, 9), (16, 11)} | {(3, 0), (5, 4), (7, –8), (9, 12), (11, 16)} |
| Find the inverse of {(3, 0), (5, 4), (7, –8), (9, 12), (11, 16)}. | {(0, 3), (4, 5), (–8, 7), (12, 9), (16, 11)} |
| Is this a function? Let A = {a, b, c, d} and B= {c, d, e, f, g} R₂ = {(a, c) (a, g) (b, d) (c, e) (d, f)} | no |
| Is this a function? Let A = {a, b, c, d} and B= {c, d, e, f, g} Let R₁ = {(a, c) (b, d) (c, e)} | Yes |
| Let f be a function on set A = {1,2,3,4,5} such that f = {(1,2) (2,3),(3,4) (4,2) ,(5, 5) } | f is onto (surjective) function |
| which is not the domain of: f(x) = (3x-2) / x^(2-9x+20) x != 4, and x != 5 x != 9, and x != 8 x != 10, and x != 11 | x != 9, and x != 8 |
| Which is the correct domain of the given function: 4 5 all of the above 6 | all of the above |
| Let f be a function on set A = {1,2,3,4,5} such that f = {(1,1) (2,2),(3,3) (4,4) ,(5, 5) } | f is bijective |
| Test the validity of the argument: All cars have wheels. That vehicle has wheels. Therefore, that vehicle is a car. | Invalid |
| Test the validity of the argument: All bears are mammals. A Koala is a bear. Therefore, a Koala is a mammal. | Valid |
| All plumbers use monkey wrenches. Some mechanics don’t use monkey wrenches. Hence, some mechanics aren’t plumbers. | Valid |
| Test the validity of the argument: All U.S. voters must register. All people who register must be U.S. citizens. Therefore, all U.S. voters are U.S. citizens. | Valid |
| It shows all possible logical relationships between a collection of sets. | Venn Diagram |
| Test the validity of the argument: All teachers are rich. Peter is a teacher. Therefore, Peter is rich. | Valid |
| It is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. | Euler Diagram |
| Test the validity of the argument: All math teachers love chocolate. Anna loves chocolate. Therefore, Anna is a math teacher. | Invalid |
| Test the validity of the argument: Some clowns have red noses. My uncle has red nose. Therefore, my uncle is a clown. | Invalid |
| Test the validity of the argument: All football players are strong. Juan is strong. Therefore, Juan is a football player. | Invalid |
| Some poodles are dogs. All poodles yap too much. Thus, some dogs yap too much. | Valid |
| Test the validity of the argument: All horses are brown. All brown animals have fur. Therefore, all horses have fur. | Valid |
| Test the validity of the argument: Some mammals live in the ocean. My dog is a mammal. Therefore, my dog lives in the ocean. | Invalid |
| Test the validity of the argument: All cats are animals. Figgy is a cat. Therefore, Figgy is an animal. | Valid |
| Test the validity of the argument: All students have cellphones. All cellphones are annoying. Therefore, all students are annoying. | Valid |
| Test the validity of the argument: All people who arrive late cannot perform. All people who cannot perform are ineligible for scholarships. Therefore, all people who arrived late are ineligible for scholarships. | Valid |
| All senators are politicians. Some corrupt people aren’t politicians. Therefore, some corrupt people aren’t senators. | Valid |
| All spies are secretive. Some agents aren’t spies. Therefore, some agents aren’t secretive. | Valid |
| Test the validity of the argument: All runners are athletes. Mary is a runner. Mary is an athlete. | Valid |
| Test the validity of the argument: All men are mortal. Peter is a man. Therefore, Peter is mortal. | Valid |
| Test the validity of the argument: No cats are green. Patty is not a cat. Therefore, Patty is green. | Invalid |
| Test the validity of the argument: All children love to swim. Maria loves to swim. Therefore, Maria is a child. | Invalid |
| All trucks are vehicles. I drive a truck. Therefore I drive a vehicle. | Valid |
| Test the validity of the argument: All teachers are smart. Angel is a teacher. Therefore, Angel is smart. | Valid |
| Test the validity of the argument: All teachers are cool. Some guys are teachers. Some guys are cool. | Valid |
| Test the validity of the argument: All sunny days are hot. Today is not hot. Today is not sunny. | Valid |
| All astronauts are bold. Some pilots are not bold. Therefore, some astronauts are not pilots. | Invalid |
| Test the validity of the argument: Some students drink coffee. I am a student. Therefore, I drink coffee. | Invalid |
| Test the validity of the argument: All runners are athletes. Sue is not an athlete. | Valid |
| Some ants are aggressive. All ants are insects. Therefore, some insects are aggressive. | Valid |
| Test the validity of the argument: All math teachers love coffee. Angel is a math teacher. Therefore, Angel loves coffee. | Valid |
| Boots are a type of footwear. I wear footwear. Therefore, I wear boots. | Valid |
| Test the validity of the argument: All cats have fur. My dog has fur. Therefore, my dog is a cat. | Valid |
| Test the validity of the argument: All runners are athletes. Linda is an athlete. Therefore, Linda is a runner. | Valid |
Created by:
AdoKwatro