Which one of the following Boolean expressions is a tautology?
Which one of the following Boolean expressions is a tautology? Correct Answer (p ∨ q) ∨ (p ∨ ~q)
A tautology is a proposition that is always true.
|
p |
q |
~p |
~q |
p ∧ q |
p ∨ q |
p ∨ ~q |
P ∧ ~q |
~p ∨ ~q |
|
T |
T |
F |
F |
T |
T |
T |
F |
F |
|
T |
F |
F |
T |
F |
T |
T |
T |
T |
|
F |
T |
T |
F |
F |
T |
F |
F |
T |
|
F |
F |
T |
T |
F |
F |
T |
F |
T |
Option (a):
|
p ∧ q |
p ∧ ~q |
(p ∧ q) ∨ (p ∧ ~q) |
|
T |
F |
T |
|
F |
T |
T |
|
F |
F |
F |
|
F |
F |
F |
Option (b):
|
(p ∨ q) |
(p ∨ ~q) |
(p ∨ q) ∨ (p ∨ ~q) |
|
T |
T |
T |
|
T |
T |
T |
|
T |
F |
T |
|
F |
T |
T |
Option (c):
|
(p ∨ q) |
(p ∨ ~q) |
(p ∨ q) ∧ (p ∨ ~q) |
|
T |
T |
T |
|
T |
T |
T |
|
T |
F |
F |
|
F |
T |
F |
Option (d):
|
(p ∨ q) |
(~p ∨ ~q) |
(p ∨ q) ∧ (~p ∨ ~q) |
|
T |
F |
F |
|
T |
T |
T |
|
T |
T |
T |
|
F |
T |
F |
From the given options, the table in option (b) is always true.
Thus, the option (b) is tautology.
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Feb 20, 2025