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Byju's Answer
Standard XII
Mathematics
Distributive Law
Using the tru...
Question
Using the truth table, prove the following logical equivalence:
p
↔
q
≡
(
p
∧
q
)
∨
(
∼
p
∧
∼
q
)
.
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Solution
p
q
p
↔
q
p
∧
q
∼
p
∼
q
∼
p
∧
∼
q
(
p
∧
q
)
∨
(
∼
p
∧
∼
q
)
T
T
T
T
F
F
F
T
T
F
F
F
F
T
F
F
F
T
F
F
T
F
F
F
F
F
T
F
T
T
T
T
From column
3
and
8
we get
p
↔
q
≡
(
p
∧
q
)
∨
(
∼
p
∧
∼
q
)
Hence proved.
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