Mathematics - Mathematical Reasoning Question with Solution | TestHub

a)\ $\mathrm{p}\to (\mathrm{q}\to \mathrm{p})\equiv \mathrm{p}\to (\sim \mathrm{q}\vee \mathrm{p})\equiv \sim \mathrm{p}\vee (\sim \mathrm{q}\vee \mathrm{p})\equiv (\sim \mathrm{p}\vee \mathrm{p})\vee \sim \mathrm{q}\equiv \mathrm{t}\vee \sim \mathrm{q}\equiv \mathrm{t}$ b) $\mathrm{p}\to (\mathrm{p}\vee \mathrm{q})\equiv \sim \mathrm{p}\vee (\mathrm{p}\vee \mathrm{q})\equiv \mathrm{t}\vee \mathrm{q}\equiv \mathrm{t}$ c) $\mathrm{p}\vee \mathrm{q}\to (\sim \mathrm{p}\wedge \sim \mathrm{q})\equiv \sim (\mathrm{p}\vee \mathrm{q})\vee (\sim (\mathrm{p}\vee \mathrm{q}))\equiv \sim (\mathrm{p}\vee \mathrm{q})$ d) $(\mathrm{p}\vee \sim \mathrm{p})\to (\mathrm{q}\wedge \sim \mathrm{q})\equiv \mathrm{t}\to \mathrm{c}\equiv (\sim \mathrm{t}\vee \mathrm{c})\equiv \mathrm{c}\vee \mathrm{c}\equiv \mathrm{c}$