Negation of the Boolean statement (p∨q)⇒((~r)∨p) is equivalent to:

P∨q⇒(~r∨p)≡∼(p∨q)∨(~r∨p)≡(~p∧~q)∨(p∨~r)≡[~p∨p)∧(~q∨p)]∨~r≡[~q∨p)∨~rIts negation is (~p)∧q∧r

Negation of the Boolean statement (p∨q)⇒((~r)∨p) is equivalent to:

P∨q⇒(~r∨p)≡∼(p∨q)∨(~r∨p)≡(~p∧~q)∨(p∨~r)≡[~p∨p)∧(~q∨p)]∨~r≡[~q∨p)∨~rIts negation is (~p)∧q∧r

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Negation of the Boolean statement $(p \lor q) \Rightarrow ((~ r) \lor p)$ is equivalent to:

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$p \land (~ q) \land r$

$(~ p) \land (~ q) \land r$

$(~ p) \land q \land r$

$p \land q \land (~ r)$

answer is C.

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Detailed Solution

$\begin{array}{l} P \lor q \Rightarrow (~ r \lor p) \\ \equiv\sim (p \lor q) \lor (~ r \lor p) \\ \equiv (~ p \land ~ q) \lor (p \lor ~ r) \\ \equiv [~ p \lor p) \land (~ q \lor p)] \lor ~ r \\ \equiv [~ q \lor p) \lor ~ r \end{array}$
Its negation is $(~ p) \land q \land r$