.

Also, is the inverse of a statement always true?

The inverse is not true juest because the conditional is true. The inverse always has the same truth value as the converse. If the conditional is true then the contrapositive is true. A pattern of reaoning is a true assumption if it always lead to a true conclusion.

Subsequently, question is, can a statement and its negation both be false? Sometimes in mathematics it's important to determine what the opposite of a given mathematical statement is. This is usually referred to as "negating" a statement. One thing to keep in mind is that if a statement is true, then its negation is false (and if a statement is false, then its negation is true).

Also Know, what is the inverse of a statement?

Inverse of a Conditional. Negating both the hypothesis and conclusion of a conditional statement. For example, the inverse of "If it is raining then the grass is wet" is "If it is not raining then the grass is not wet". Note: As in the example, a proposition may be true but its inverse may be false.

What is the Contrapositive of P → Q?

The contrapositive of a conditional statement of the form "If p then q" is "If ~q then ~p". Symbolically, the contrapositive of p q is ~q ~p. A conditional statement is logically equivalent to its contrapositive.