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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 94
Question 94 of 103
Medium
MCQ
Let \[\Delta ,\nabla \in \{ \wedge , \vee \} \] be such that \[\mathrm{(p \to q)\Delta (p\nabla q)}\] is a tautology. Then
A
\[\Delta = \vee ,\nabla = \vee \]
B
\[\Delta = \vee ,\nabla = \wedge \]
C
\[\Delta = \wedge ,\nabla = \wedge \]
D
\[\Delta = \wedge ,\nabla = \vee \]
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Official solution
(
p
⟶
q
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Δ
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∇
q
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(p \longrightarrow q) \Delta(p \nabla q)
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Δ
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⇒
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′
∨
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Δ
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.
.
.
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i
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\Rightarrow \left(p^{\prime} \vee q\right) \Delta(p \nabla q)\quad...(i)
⇒
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∨
q
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Δ
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...
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\[ \text { If } \Delta=v, \nabla=v \] (i) becomes
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∨
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≡
T
\left(p^{\prime} \vee q\right) \vee(p \vee q) \equiv T
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∨
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≡
T
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