If you replace all ∨ with addition and ∧ with multiplication, which logical equivalence still holds? A) Distributive law B) Idempotent law C) De Morgan's law D) Double negation
Understand the Problem
The question is asking which logical equivalence remains valid when logical operators are replaced with arithmetic operations: '∨' (OR) with addition and '∧' (AND) with multiplication. We need to evaluate the listed options to determine the correct logical equivalence that holds under these replacements.
Answer
Distributive law
The final answer is Distributive law
Answer for screen readers
The final answer is Distributive law
More Information
The Distributive law in logic (p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)) holds when ∨ is replaced with addition and ∧ is replaced with multiplication, reflecting the distributive property of addition over multiplication in arithmetic.
Sources
- 2.5: Logical Equivalences - Mathematics LibreTexts - math.libretexts.org
- Can't understand the solution given on logical equivalence - math.stackexchange.com
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