(a) A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.
(b) A converse statement is gotten by exchanging the positions of 'p' and 'q' in the given condition. if p→q, p → q , then, q→p. For example, "If Cliff is thirsty, then she drinks water" is a condition. The converse statement is "If Cliff drinks water, then she is thirsty."
(c) In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form {\displaystyle P\rightarrow Q}, the inverse refers to the sentence {\displaystyle \neg P\rightarrow \neg Q}.
(d) To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain." If p , then q .
