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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 40
Question 40 of 103
Easy
MCQ
The negation of the Boolean expression p \[ \vee \] (~p \[ \wedge \] q) is equivalent to :
A
\[p \wedge \sim q\]
B
\[ \sim \]
p
∨
∼
q
p \vee \sim q
p
∨
∼
q
C
\[ \sim p \wedge q\]
D
\[ \sim p \wedge \sim q\]
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Official solution
p \[ \vee \] (~p \[ \wedge \] q) = (p \[ \vee \] ~p) \[ \wedge \] (p \[ \vee \] q) = (T) \[ \wedge \] (p \[ \vee \] q) = (p \[ \vee \] q) Now negation of (p \[ \vee \] q) is \[ \sim (p \[ \vee \] q) = \[ \sim p \wedge \sim q\]
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