The number of distinct simple graph with upto three nodes is

Let $$p$$ and $$q$$ be propositions. Using only the truth table decide whether $$p \Leftrightarrow q$$ does not imply $$p \to \sim q$$ is true or false.

The number of substrings (of all length inclusive) that can be formed from a character string of length $$n$$ is

Let A and B be any two arbitrary events, then, which one of the following is true?