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Question Number 178568 by Spillover last updated on 18/Oct/22

$$\mathrm{Given}\mathrm{the}\mathrm{preposition}$$$$[(\mathrm{p}\to \mathrm{q})\wedge (\mathrm{q}\to \mathrm{r})]\to (\mathrm{p}\to \mathrm{r})$$$$\mathrm{Write}\mathrm{down}$$$$\left(\mathrm{a}\right)\mathrm{Converse}$$$$\left(\mathrm{b}\right)\mathrm{Inverse}$$$$\left(\mathrm{c}\right)\mathrm{Contrapositive}$$

Answered by cortano1 last updated on 18/Oct/22

$$\left(\mathrm{a}\right)(\mathrm{p}\Rightarrow \mathrm{r})\Rightarrow [(\mathrm{p}\Rightarrow \mathrm{q})\wedge (\mathrm{q}\Rightarrow \mathrm{r})]$$$$\left(\mathrm{b}\right)[(\mathrm{p}\wedge \sim \mathrm{q})\vee (\mathrm{q}\wedge \sim \mathrm{r})]\Rightarrow (\mathrm{p}\wedge \sim \mathrm{r})$$$$\left(\mathrm{c}\right)(\mathrm{p}\wedge \sim \mathrm{r})\Rightarrow [(\mathrm{p}\wedge \sim \mathrm{r})\vee (\mathrm{q}\wedge \sim \mathrm{r})]$$

Commented by Spillover last updated on 18/Oct/22

$$\mathrm{thanks}$$

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