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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 24
Question 24 of 103
Medium
MCQ
Which one of the following Boolean expressions is a tautology?
A
(p \[ \vee \] q) \[ \wedge \] (~ p \[ \vee \] ~ q)
B
(p \[ \vee \] q) \[ \vee \] ( p \[ \vee \] ~ q)
C
(p \[ \wedge \] q) \[ \vee \] ( p \[ \wedge \] ~ q)
D
(p \[ \vee \] q) \[ \wedge \] ( p \[ \vee \] ~ q)
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Official solution
(p \[ \vee \] q) \[ \vee \] (p \[ \vee \] ~ q) = p \[ \vee \] (q \[ \vee \] p) \[ \vee \] ~ q = (p \[ \vee \] p) \[ \vee \] (q \[ \vee \] ~ q) = p \[ \vee \] T = T so first statement is tautology
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