Which of the following sentences is equivalent to p q ppppq

Which of the following sentences is equivalent to (p q)? ((p|p)|(p|p)|q)) (((p|p)|q)|(q|q)) ((p|(q|q))|(p|(q|q)) (((P|p)|(q|q))|(p|q))

Solution

The question is (p bi implies q) that is  If p and q have the same truth value, the biconditional p <=> q is true; if p and q have opposite truth values then
p <=> q is false.

Now if we see the options,by the laws that govern truth table algebras, every option comes out to be p|q (read as p or q) as | symbol stands for \"or\" . And hence when the truth table of both are observed, they dont completely match and hence non of the options match