Mathematics - Mathematical Reasoning Question with Solution | TestHub

Given propositions ${\mathrm{P}}_1:\sim (\mathrm{p}\to \sim \mathrm{q})$ ${\mathrm{P}}_2:(p\wedge \sim q)\wedge ((\sim p)\vee q)$ Required table is shown below. $\begin{array}{llllllllll}\mathbf{p}& \mathbf{q}& \sim p& \sim q& \sim p\vee q& p\to (\sim (p\vee q)& p\to \sim q& \sim (p\to \sim q)& p\wedge \sim q& p_2\\ \text{ T }& \text{ T }& \text{ F }& \text{ F }& \text{ T }& \text{ T }& \text{ F }& \text{ T }& \text{ F }& \text{ F }\\ \text{ T }& \text{ F }& \text{ F }& \text{ T }& \text{ F }& \text{ F }& \text{ T }& \text{ F }& \text{ T }& \text{ F }\\ \text{ F }& \text{ T }& \text{ T }& \text{ F }& \text{ T }& \text{ T }& \text{ T }& \text{ F }& \text{ F }& \text{ F }\\ \text{ F }& \text{ F }& \text{ T }& \text{ T }& \text{ T }& \text{ T }& \text{ T }& \text{ F }& \text{ F }& \text{ F }\end{array}$ $p\to (\sim p\vee q)$ is $F$ when $p$ is true $q$ is false From table $P_1\&P_2$ both are false