p: Sun is shining
q: I shall play in afternoon
​Negation of "If sun is shining, then i shall play in the afternoon" is:
​a) p^~q  b) q--> ~p  c) ~q--> ~p  d) q^ ~p

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{p}: \mathrm{Sun} \mathrm{is} \mathrm{shining} \\ \mathrm{q}: \mathrm{I} \mathrm{shall} \mathrm{play} \mathrm{in} \mathrm{afternoon} \\ \mathrm{Now} \\ \mathrm{If} \mathrm{sun} \mathrm{is} \mathrm{shining}, \mathrm{then} \mathrm{i} \mathrm{shall} \mathrm{play} \mathrm{in} \mathrm{the} \mathrm{afternoon} \mathrm{is} \mathrm{p}\to \mathrm{q} \\ \mathrm{We} \mathrm{know} \mathrm{that} \\ \mathrm{Negation} \mathrm{of} \mathrm{p}\to \mathrm{q} \mathrm{is} \mathrm{given} \mathrm{by} \\ ~\left(\mathrm{p}\to \mathrm{q}\right)=\mathrm{p}^ ~\mathrm{q} \\ \mathrm{Hence} \mathrm{option}\left(\mathrm{a}\right) \mathrm{is} \mathrm{correct}. \end{gathered}$$

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