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Using the Truth Table, Prove the Following Logical Equivalence : P ↔ Q ≡ (P ∧ Q) ∨ (~P ∧ ~Q ) - Mathematics and Statistics

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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

 2017-2018 (March) (with solutions)
Question 2.1.2 | 3.00 marks
Solution Using the Truth Table, Prove the Following Logical Equivalence : P ↔ Q ≡ (P ∧ Q) ∨ (~P ∧ ~Q ) Concept: Mathematical Logic - Truth Tables of Compound Statements.
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