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# If p,q,r are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true, then

$\begin {array} {1 1} (A)\;p,q,r \: are\: all \: false & \quad (B)\;p,q,r\: are\: all \: true \\ (C)\;p,q \: are\: true\: and\: r\: is\: false & \quad (D)\;p \: is\: true\: and\: q,r\: are\: false \end {array}$

Ans : (B)
$(p \wedge q) \wedge (q \wedge r)$ is true means $p \wedge q,\: q \wedge r$
are both true, it implies that p,q,r are all true.