Testbank for Discrete Mathematics: Proofs, Structures and Applications (3rd Edition, 2026) – Solutions to Exercises – Garnier

Discrete Mathematics: Proofs, Structures and
Applications (3rd Edition, 2026) – Solutions to
Exercises – Garnier

p v q - answers-This is a disjunction: p or q, or p and q. This is an inclusive or.



p ^ q - answers-This is a conjunction: p and q



p ⊕ q - answers-This is an exclusive or: either p or q



p → q - answers-This is an implication. If p, then q



Converse conditional statements - answers-q → p



Contrapositive conditional statements - answers-¬q → ¬p (has the same truth values as p → q)



Inverse conditional statement - answers-¬p → ¬q



p ↔ q - answers-This is a biconditional statement, also known as bi-implications. It means p if
and only if q. True if both p and q have the same truth values. Also written as "p is necessary
and sufficient for q", "if p then q, and conversely", and "p iff q".



Precedence of logical operators in 1st to 5th - answers-1. ¬ 2. ^ 3. v 4. → 5. ↔




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, Bit - answers-This is a symbol with two possible values, specifically 0 (zero) and 1 (one). 1
represents the True value and 0 represents a False value.



De Morgan's law - answers-When you distribute a "¬", then you flip the conjunction or
disjunction sign that you are distributing to.



p∧T≡p

p ∨ F ≡ p - answers-Identity laws



p∨T≡T

p ∧ F ≡ F - answers-Domination laws



p∨p≡p

p ∧ p ≡ p - answers-Idempotent laws



¬(¬p) ≡ p - answers-Double negation law



p∨q≡q∨p

p ∧ q ≡ q ∧ p - answers-Commutative laws



(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r) - answers-Associative laws



p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) - answers-Distributive laws


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