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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
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
