Question

If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?

Options

• \[(p\wedge q)\]

• \[(p\vee r)\]

• \[(p\wedge r)\]

• \[(p\wedge r)\rightarrow(p\vee r)\]

Answer 1

\[(p\wedge r)\rightarrow(p\vee r)\]

Explanation:

Since q is \[\mathrm{F\Rightarrow p\wedge q\equiv F}\]

Since \[\mathrm{(p\wedge q)\leftrightarrow r~is~F\Rightarrow r\equiv F}\]

p can be T or F

\[(p\wedge r)\] will always be F

\[\Rightarrow(\mathfrak{p}\wedge\mathfrak{r})\to(\mathfrak{p}\vee\mathfrak{r})\] will always be T.