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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 77
Question 77 of 103
Easy
MCQ
Which of the following statement is a tautology?
A
\[(( \sim q) \wedge p) \wedge q\]
B
\[(( \sim q) \wedge p) \wedge (p \wedge ( \sim p))\]
C
\[(( \sim q) \wedge p) \vee (p \vee ( \sim p))\]
D
\[(p \wedge q) \wedge ( \sim p \wedge q))\]
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Official solution
\[\because\] ((\[\sim\] q) \[\wedge\] p) \[\vee\] (p \[\vee\] (\[\sim\] p)) = (\[\sim\] q \[\wedge\] p) \[\vee\] t (t is tautology) \[\equiv\] t \[\therefore\] option (C) is correct.
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