Busy. Please wait.

show password
Forgot Password?

Don't have an account?  Sign up 

Username is available taken
show password


Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.
We do not share your email address with others. It is only used to allow you to reset your password. For details read our Privacy Policy and Terms of Service.

Already a StudyStack user? Log In

Reset Password
Enter the associated with your account, and we'll email you a link to reset your password.
Don't know
remaining cards
To flip the current card, click it or press the Spacebar key.  To move the current card to one of the three colored boxes, click on the box.  You may also press the UP ARROW key to move the card to the "Know" box, the DOWN ARROW key to move the card to the "Don't know" box, or the RIGHT ARROW key to move the card to the Remaining box.  You may also click on the card displayed in any of the three boxes to bring that card back to the center.

Pass complete!

"Know" box contains:
Time elapsed:
restart all cards
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

  Normal Size     Small Size show me how

Exam 1

MAT 300 Mathematical Structures

Def: Tautology Formulas that are always true ex) P or not P
Def: Contradiction Formulas that are always false ex) P and not P
Def: Converse The reversal of an if-then statement. Logically equivalent to inverse. ex) P -> Q ; Q -> P
R The set of all real numbers, containing all rational and irrational numbers. Q, N , Z are the subsets of the set R.
Q The set of all rational numbers. The rational numbers are any number which could be written like p/q, where p and q are integers.
N The set of all natural numbers like:1,2,3,4,5,....... The set has starting number 1 and the consecutive numbers increments by 1 . It has no end.
Z Integers (positive or negatives including zero).
Def: Statement An assertion (about mathematics) that is objectively either true or false
Def: Argument A sequence of statements. All except the last are premises, while the last is a conclusion.
Def: Valid Argument P1, P2, P3, ... , Pk | Q Q is true when all Ps are true (conclusion is true whenever all premises are true
Def: Proof of an Assertion Q A sequence of true statements connected with valid arguments and ending with Q
Def: Equivalence Two statements with the same truth table Symbol: <=>
Def: Set A collection of objects (elements)
Free Variables Truth value depends on variable
Bound Variables Variable can be replaced or eliminated
DeMorgan's Law ~(A or B) --> ~A and ~B ~(A and B) --> ~A or ~B
Def: Contrapositive Reversing if-then and adding "not" to both sides (combines inverse and converse). Logically equivalent to conditional! ex) P --> Q ; ~Q --> ~P
Def: Inverse Adds not to both sides. Logically equivalent to converse.
Def: Power Set The set whose elements are all subsets of A P(A) = { x | x is a subset of A }
Commutative Laws P ^ Q is equivalent to Q ^ P P or Q is equivalent to Q or P
Associative Laws When a statement has all "and"s or "or"s, it doesn't matter how you separate them P ^ (Q ^ R) is equivalent to (P ^ Q) ^ R P or (Q or R) is equivalent to (P or Q) or R
Idempotent Laws P and/or P is equivalent to P
Distributive Laws P ^ (Q or R) is equivalent to (P ^ Q) or (P ^ R) P or (Q ^ R) is equivalent to (P or Q) ^ (P or R)
Absorption Laws P or (P ^ Q) is equivalent to P P ^ (P or Q) is equivalent to P
Modus Ponens If you know that P is true and P --> Q is true, then Q is also true
Modus Tollens If you know that P --> Q is true and Q is false, then Q is false
Proof by Contradiction Show that if a proposition is false, a contradiction is implied
Def: Elements Objects in sets
Created by: arianaflores