Question | Answer |
Logic | The study of reasoning. Allow us to determine if a statement is true, false, or uncertain. |
Open Sentence | Contains no truth value. Contains a variable. |
3x+2=7 | Open Sentence |
10+4=15 | Closed Sentence |
Hannah has blue eyes. | Closed Sentence |
She has blue eyes. | Open Sentence |
Negatation | (~) place not in the statement or remove it. A statement and it's negatation have opposite truth values. |
Conjunction | Compound sentence formed by using and. (^) Only true when both parts are true. |
Disjunction | A compound sentence formed by using or (v) Only false when both parts are false. Only needs at least one true. |
Conditional | A compound sentence using if....then or implies (➡) |
Biconditional | (p ➡ q)^(q ➡ p) if and only if or (p ⬅➡ q) True when both parts match. |
Hypothesis | Follows if |
Conclusion | Follows then |
Consiquent | Another word for conclusion |
Compound Statement | T,F,T,F Sentence that is a mixture of true and false |
Tautology | Compound sentence that is always going to be true T,T,T,T |
Logically Equivalent | 2 statements that always have the same truth value. If it is logically equivalent it is tautology. |
Law of Detachment | R ➡ ~W
R
________
~W |
Conditional (original) | P ➡ Q |
Converse | Q ➡ P Switch |
Inverse | ~P ➡ ~Q Negate |
Contrapositive | ~Q ➡ ~P Switch and Negate |
A conditional and it's contrapositive always have same truth value | Logically Equivalent |
The converse and its inverse always have the same truth value | Logically Equivalent |
Law | Any thing that is true |
Given/ Premise | Always true |
Modus Tollens | A conditional Premise
Negation of the Conclusion
____________________________
Conclude Negation of Hypothesis |
What is the difference between Law of Detachment and Modus Tollens? | In law of deatchment same symbols line up.
P➡Q
P
______
Q |
Modus Tollens= | Contrapositive and Law of Detachment |