Q5 / 69 · NTA Abhyas (JEE Main) 2020 · Mathematics · Mathematical Reasoning

If $p, q$ and $r$ are three logical statements then the truth value of the statement $(p \land ~ q) \lor (q \to r)$ , where $p$ is true, is

A
True if $q$ is true
B
False if $q$ is true
Correct answer
C
True if $q$ is false
D
False if $q$ is false

Solution

Clearly, if

q

is False,

p

is True, then

(p \land ~ q)

is True
Hence,

(p \land ~ q) \lor (q \to r)

is True irrespective of

r

Hence, the correct answer is option: 'C'.

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