Discrete Mathematics Exam 1 Questions and Answers 100% Solved

©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.

Discrete Mathematics Exam 1 Questions

and Answers 100% Solved


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

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

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

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

Converse conditional statements - ✔✔q → p

Contrapositive conditional statements - ✔✔¬q → ¬p (has the same truth

values as p → q)

Inverse conditional statement - ✔✔¬p → ¬q

p ↔ q - ✔✔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 - ✔✔1. ¬ 2. ^ 3. v 4. → 5. ↔

, ©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.

Bit - ✔✔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 - ✔✔When you distribute a "¬", then you flip the

conjunction or disjunction sign that you are distributing to.

p∧T≡p

p ∨ F ≡ p - ✔✔Identity laws

p∨T≡T

p ∧ F ≡ F - ✔✔Domination laws

p∨p≡p

p ∧ p ≡ p - ✔✔Idempotent laws

¬(¬p) ≡ p - ✔✔Double negation law

p∨q≡q∨p

p ∧ q ≡ q ∧ p - ✔✔Commutative laws

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

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

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

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