If p, q and r are any three logical statements, then which one of the following is correct ?

Let p,q and r be any three logical statements. Which one of the following is true?

If p is any logical statement, then

If p is any logical statement, then

Let p:57 is an odd prime number, q : 4 is a divisor of 12, r : 15 is the LCM of 3 and 5 be three simple logical statements. Which one of the following is true ? a) p vv (~ q ^^ r) b) ~p vv (q ^^ r) c) (p ^^ q) vv ~ r d) (p vv q) ^^ ~r

If p, q are r are three logical statements, then the truth value of the statement (p^^q)vv (~q rarr r) , where p is true, is