Question
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q )
Solution
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
A | B | ||||||
p | q | p ↔ q | p ∧ q | ~p | ~q | ~p ∧ ~q | A V B |
T T F F |
T F T F |
T F F T |
T F F F |
F F T T |
F T F T |
F F F T |
T F F T |
By column number 3 and 8
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q )
Is there an error in this question or solution?
APPEARS IN
Solution Using the Truth Table, Prove the Following Logical Equivalence : P ↔ Q ≡ (P ∧ Q) ∨ (~P ∧ ~Q ) Concept: Mathematical Logic - Truth Tables of Compound Statements.