Q.Verify by the method of contradiction $p : \sqrt{7}$ is irrational.

The method of contradiction proves that a statement p is true by doing the opposite of what seems natural: assume that p is FALSE, i.e., assume $\sim p$ is true, and reason forward from that assumption using valid logical steps until the reasoning runs into something impossible — a contradiction of a known fact, of an assumption already made, or of the very statement $\sim p$ itself. Since assuming $\sim p$ leads to an impossibility, $\sim p$ cannot actually be true, and therefore p must be true. A classic illustration is proving that $\sqrt{7}$ is irrational: assume instead that $\sqrt{7}$ IS rational, express it as a fraction in …