Given-the-preposition-p-q-q-r-p-r-Write-down-a-Converse-b-Inverse-c-Contrapositive-

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

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

Answered by cortano1 last updated on 18/Oct/22

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

Commented by Spillover last updated on 18/Oct/22

$$\mathrm{thanks} \\ $$

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