If p,q and r are three propositions, then which of the following combination of truth valu…

Question

If $p,q$ and $r$ are three propositions, then which of the following combination of truth values of $p,q$ and $r$ makes the logical expression $$\left\{ {(p \vee q) \wedge \left( {( \sim p) \vee r} \right)} \right\} \to \left( {( \sim q) \vee r} \right)$$ false?

Accepted Answer

$\mathrm{p}$
    $\mathrm{q}$
    $\mathrm{r}$
    $(p \vee q) \wedge((\sim p) \vee r)$
    $\sim \mathrm{q} \vee \mathrm{r}$

$(1)$
    $\mathrm{T}$
    $\mathrm{F}$
    $\mathrm{T}$
    $\mathrm{T}$
    $\mathrm{T}$

$(2)$
    $\mathrm{T}$
    $\mathrm{T}$
    $\mathrm{F}$
    $\mathrm{F}$
    $\mathrm{F}$

$(3)$
    $\mathrm{F}$
    $\mathrm{T}$
    $\mathrm{F}$
    $\mathrm{T}$
    $\mathrm{F}$

$(4)$
    $\mathrm{T}$
    $\mathrm{F}$
    $\mathrm{F}$
    $\mathrm{F}$
    $\mathrm{T}$

So, $(p \vee q) \wedge(\sim q \vee r) \rightarrow(\sim p \vee r)$ will be False.

Solutions · 1