Discrete Math Study Guide Questions with Correct Answers

Discrete Math Study Guide Questions with
Correct Answers
Proposition

Declarative sentence (True or False)

Conjunction

and

Disjunction

or

Negation

not

Exclusive Or

p or q but not both

Implication

p-->q

- a conditional statement

- if p then q

- q is necessary for p

Converse (p-->q)

q-->p (with respect to p --> q)

Contrapositive (p-->q)

¬q --> ¬p (with respect to p -->q )

,Inverse (p-->q)

¬p --> ¬q (with respect to p -->q)

Precedence of Logical Operators

Not

And

Or

Implies

If and Only If

Biconditional

p<-->q

If and only if

- both need to be true in order for the statement to be true



- (p-->q) V (q-->p)

Rows

2^n

n = propositional values

Columns

Needed for each propositional phrase

Tautology

A statement that is always true

- p or not p

,Contradiction

A statement that is never true

- p and not p

Contingency

A proposition that is neither a tautology nor a contradiction

Logical Equivalent

when the biconditional of p and q is always true

≡

Identity Laws

p∧T≡p

p∨F≡p


Domination Laws

p∨T≡T

p∧F≡F


Idempotent Laws

p∨p≡p

p∧p≡p


Double Negation Law

¬(¬p) ≡ p

Negation Laws

, p ∨ ¬p ≡ T

p ∧ ¬p ≡ F


Communative Law

p∨q≡qVp

p∧q≡q∧p


Associative Laws

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

Distributive Laws

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


Absorption Laws

p ∨ (p ∧ q) ≡ p

p ∧ (p ∨ q) ≡ p


De Morgan's laws (proposition logical)

¬(p ∧ q) ≡ (¬p V ¬q)

¬(p V q) ≡ (¬p ∧ ¬q)


p --> q ≡

¬p V q

OR

¬q V p