First slide

Introduction to mathematical reasoning

Question

Which of the following is true for the statements p and q ?

Moderate

A

$p \land q$ is true when at least one of p and g is true
B

$p \to q$ is true when p is true and q is false
C

$p \leftrightarrow q$ is true only when both p and q are true
D

$~ (p \lor q)$ is false only when both p and q are false

Solution

(a) We know that, $p \land q$ is true when both p and q are true.
(b) We know that, $p \to q$ is false when p is true and g is false.
(c) We know that, $p \leftrightarrow q$ is true when either both p and q are true or both are false.
(d) If p and g both are false, then $p \lor q$ is false $\Rightarrow\sim (p \lor q)$ is true.
Hence, option (d) is true.

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