Logical Equivalence

claude

Implication Law — what is the equivalent form of p → q?

¬p ∨ q (Conditional equivalence)

Contrapositive Law — what is the equivalent form of p → q?

¬q → ¬p (Same truth values)

Double Negation Law — what is the equivalent form of ¬(¬p)?

p (Two negations cancel)

De Morgan's Law (1) — what is the equivalent form of ¬(p ∧ q)?

¬p ∨ ¬q (Negation of AND becomes OR)

De Morgan's Law (2) — what is the equivalent form of ¬(p ∨ q)?

¬p ∧ ¬q (Negation of OR becomes AND)

Distributive Law — what is the equivalent form of p ∧ (q ∨ r)?

(p ∧ q) ∨ (p ∧ r) (Works like algebra)

Commutative Law — what is the equivalent form of p ∨ q?

q ∨ p (Order doesn't matter)

Associative Law — what is the equivalent form of (p ∨ q) ∨ r?

p ∨ (q ∨ r) (Grouping doesn't matter)

Absorption Law (1) — what is the equivalent form of p ∨ (p ∧ q)?

p (Redundant term absorbed)

Absorption Law (2) — what is the equivalent form of p ∧ (p ∨ q)?

p (Redundant term absorbed)

Here are the reverse-direction cards to add to your set:

What law/rule states that ¬p ∨ q is equivalent to p → q?

Implication Law

What law/rule states that ¬q → ¬p is equivalent to p → q?

Contrapositive Law

What law/rule states that p is equivalent to ¬(¬p)?

Double Negation Law

What law/rule states that ¬p ∨ ¬q is equivalent to ¬(p ∧ q)?

De Morgan's Law (1)

What law/rule states that ¬p ∧ ¬q is equivalent to ¬(p ∨ q)?

De Morgan's Law (2)

What law/rule states that (p ∧ q) ∨ (p ∧ r) is equivalent to p ∧ (q ∨ r)?

Distributive Law

What law/rule states that q ∨ p is equivalent to p ∨ q?

Commutative Law

What law/rule states that p ∨ (q ∨ r) is equivalent to (p ∨ q) ∨ r?

Associative Law

What law/rule reduces p ∨ (p ∧ q) down to just p?

Absorption Law (1)

What law/rule reduces p ∧ (p ∨ q) down to just p?

Absorption Law (2)

Here are the fill-in-the-blank style cards to round out the set:

p → q ≡ ___

¬p ∨ q (Implication Law)

p → q ≡ ___ (using contraposition)

¬q → ¬p (Contrapositive Law)

¬(¬p) ≡ ___

p (Double Negation Law)

¬(p ∧ q) ≡ ___

¬p ∨ ¬q (De Morgan's Law 1)

¬(p ∨ q) ≡ ___

¬p ∧ ¬q (De Morgan's Law 2)

p ∧ (q ∨ r) ≡ ___

(p ∧ q) ∨ (p ∧ r) (Distributive Law)

p ∨ q ≡ ___

q ∨ p (Commutative Law)

(p ∨ q) ∨ r ≡ ___

p ∨ (q ∨ r) (Associative Law)

p ∨ (p ∧ q) ≡ ___

p (Absorption Law 1)

p ∧ (p ∨ q) ≡ ___

p (Absorption Law 2)