DISCRETE MATHEMATICS AND ITS APPLICATIONS CERTIFICATION EVALUATION TEST COMPLETE QUESTIONS AND CORRECT ANSWERS

DISCRETE MATHEMATICS AND ITS
APPLICATIONS CERTIFICATION EVALUATION
TEST COMPLETE QUESTIONS AND CORRECT
ANSWERS

◉ Conjunction.
Answer: and


◉ Disjunction.
Answer: or


◉ Negation.
Answer: not


◉ Exclusive Or.
Answer: p or q but not both


◉ Implication.
Answer: p-->q
- a conditional statement
- if p then q

,- q is necessary for p


◉ Converse (p-->q).
Answer: q-->p (with respect to p --> q)


◉ Contrapositive (p-->q).
Answer: ¬q --> ¬p (with respect to p -->q )


◉ Inverse (p-->q).
Answer: ¬p --> ¬q (with respect to p -->q)


◉ Precedence of Logical Operators.
Answer: Not
And
Or
Implies
If and Only If


◉ Biconditional.
Answer: 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.
Answer: 2^n
n = propositional values


◉ Columns.
Answer: Needed for each propositional phrase


◉ Tautology.
Answer: A statement that is always true
- p or not p


◉ Contradiction.
Answer: A statement that is never true
- p and not p


◉ Contingency.
Answer: A proposition that is neither a tautology nor a contradiction


◉ Logical Equivalent.

, Answer: when the biconditional of p and q is always true
≡


◉ Identity Laws.
Answer: p ∧ T ≡ p
p∨F≡p


◉ Domination Laws.
Answer: p ∨ T ≡ T
p∧F≡F


◉ Idempotent Laws.
Answer: p ∨ p ≡ p
p∧p≡p


◉ Double Negation Law.
Answer: ¬(¬p) ≡ p


◉ Negation Laws.
Answer: p ∨ ¬p ≡ T
p ∧ ¬p ≡ F