# The truth values of p, q and r for which (p ∧ q) ∨ (~ r) has truth value F are respectively

1) F, T, F

2) F, F, F

3) T, T, T

4) T, F, F

5) F, F, T

Solution: (5) F, F, T

$$\begin{array}{l}\begin{array}{llllll} \text { p } & \text { q } & r & \sim r & p_{\wedge} q & (p \wedge q) \vee(\sim r) \\ \hline \text { T } & \text { T } & \text { T } & \text { F } & \text { T } & \text { T } \\ \hline \text { T } & \text { T } & \text { F } & \text { T } & \text { T } & \text { T } \\ \hline \text { T } & \text { F } & \text { T } & \text { F } & \text { F } & \text { F } \\ \hline \text { T } & \text { F } & \text { F } & \text { T } & \text { F } & \text { T } \\ \hline \text { F } & \text { T } & \text { T } & \text { F } & \text { F } & \text { F } \\ \hline \text { F } & \text { T } & \text { F } & \text { T } & \text { F } & \text { T } \\ \hline \text { F } & \text { F } & \text { T } & \text { F } & \text { F } & \text { F } \\ \hline \text { F } & \text { F } & \text { F } & \text { T } & \text { F } & \text { T } \\ \hline \end{array}\end{array}$$

Hence, (p ∧ q) ∨ (~ r) has truth value F when truth values of p, q and r are T, F, T or F, T, T or F, F, T respectively.

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