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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 45
Question 45 of 103
Medium
MCQ
Which of the following Boolean expression is a tautology?
A
(p \[ \wedge \] q) \[ \vee \] (p \[ \to \] q)
B
(p \[ \wedge \] q) \[ \vee \] (p \[\vee\] q)
C
(p \[ \wedge \] q) \[ \to \] (p \[ \to \] q)
D
(p \[ \wedge \] q) \[ \wedge \] (p \[ \to \] q)
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Official solution
\[
(
p
q
p
∧
q
p
∨
q
p
→
q
(
p
∧
q
)
→
(
p
→
q
)
T
T
T
T
T
T
F
T
F
T
T
T
T
F
F
T
F
T
F
F
F
F
T
T
)
\begin{pmatrix} p & q & {p \wedge q} & {p \vee q} & {p \to q} & {(p \wedge q) \to (p \to q)} \\ T & T & T & T & T & T \\ F & T & F & T & T & T \\ T & F & F & T & F & T \\ F & F & F & F & T & T \\ \end{pmatrix}
p
T
F
T
F
q
T
T
F
F
p
∧
q
T
F
F
F
p
∨
q
T
T
T
F
p
→
q
T
T
F
T
(
p
∧
q
)
→
(
p
→
q
)
T
T
T
T
\]
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