D420 DISCRETE MATH: LOGIC EXAM ACTUAL 2025/2026 QUESTIONS AND 100% CORRECT ANSWERS

D420 DISCRETE MATH: LOGIC EXAM ACTUAL 2025/2026 QUESTIONS AND 100% CORRECT ANSWERS proposition a statement that is either true or false ^ and v or ¬negation → conditional operation, "if p, then q" Equivalent English expressions that mean "if p, then q" If p, q q, if p p implies q p only if q p is sufficient for q q is necessary for p in a conditional proposition "→" p is the _______ and q is the __________ p is the hypothesis and q is the conclusionThe converse is the opposite of the conditional statement For example, the converse of p → q (if p then q) is q → p (if q then p). If p → q is true, it does NOT guarantee that q → p is true The inverse is the negation of the conditional statement For example, the inverse of p → q (if p then q) is ¬p → ¬q (if not p then not q). If p → q is true, it does NOT guarantee that ¬p → ¬q is true The contrapositive is the opposite and negative of the conditional statement For example, the contrapositive of p → q (if p then q) is ¬q → ¬p (if not q then not p). If p → q is true, it DOES guarantee that ¬q → ¬p is truebiconditional operation is read "p is necessary and sufficient for q" or "if p then q, and conversely" or "p if and only if q" Logical equivalence p ≡ q Two compound propositions are logically equivalent if they have the same truth value. That is, the truth value in the final column in a truth table is the same for both compound propositions tautology If the compound propositions is always true. For example, p∨¬p. contradiction if the compound proposition is always false. For example, p∧¬p.De Morgan's Law logical equivalences that show how to correctly distribute a negation operation inside a parenthesized expression containing the disjunction or conjunction operator. ¬(p ∨ q) = (¬p ∧ ¬q) ¬(p ∧ q) = (¬p ∨ ¬q) Absorption laws p ∨ (p ∧ q) ≡ p p ∧ (p ∨ q) ≡ p Associative laws (p ∨ q) ∨ r ≡ p ∨ (q ∨ r) (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)