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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 11
Question 11 of 103
Medium
MCQ
The statement \[\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)\] is
A
equivalent to \[{ \sim p \leftrightarrow q}\]
B
a tautology
C
a fallacy
D
equivalent to \[{p \leftrightarrow q}\]
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Solutions · 1
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Official solution
Making truth table (Let
(
p
∧
∼
q
)
⇒
(
p
⇒
∼
q
)
=
E
(p \wedge \sim q) \Rightarrow(p \Rightarrow \sim q)=E
(
p
∧
∼
q
)
⇒
(
p
⇒∼
q
)
=
E
)
p
p
p
q
q
q
∼
p
\sim p
∼
p
∼
q
\sim q
∼
q
p
∧
∼
q
p \wedge \sim q
p
∧
∼
q
p
⇒
∼
q
p \Rightarrow \sim q
p
⇒∼
q
E
E
E
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
∴
E
\therefore E
∴
E
is a tautology
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