Question

For any three propositions $p.$ $q$ and $r,$ the proposition
$(p\wedge q)\wedge (q\wedge r)$ is true when

• A. $p.q,r$ are all false
• B. $p.q,r$ are all true
• C. $p.q$ are true and $r$ is false
• D. $p$ is true and $q$ and $r$ are false

Answer 1

The correct option is B $p.q,r$ are all true

$\left(p\Lambda q\right)\Lambda \left(q\Lambda r\right)$ is true only when

$p,q,r$ all are true

In that case

$p\Lambda q=$ true

$q\Lambda r=$ true

$\therefore$ $\left(p\Lambda q\right)\Lambda \left(q\Lambda r\right)$ $=$ true

$\therefore$ Option B.