What is the symbol for contrapositive statement?

What is the symbol for contrapositive statement?

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.

What is the law of contrapositive example?

“If it is raining, then I wear my coat” — “If I don’t wear my coat, then it isn’t raining.” The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true.

What is the converse of the contrapositive of P → Q?

The converse of q → ~ p is ~ p → q.

What is the law of contrapositive in math?

The law of contrapositive states that the original statement is true if, and only if, the contrapositive is true. If the contrapositive is false, the original statement is false. Contrapositives are an example of conditional statements that may or may not depend on each other.

What is the contrapositive of an implication?

The contrapositive of an implication is the inverse, negated version of the implication. The implication is true if, and only if, the contrapositive is true. Are you a student or a teacher?

What are contrapositive and converse statements in mathematics?

In mathematics, we observe many statements with “if-then” frequently. For example, consider the statement. Contrapositive and converse are specific separate statements composed from a given statement with “if-then”. Before getting into the contrapositive and converse statements, let us recall what are conditional statements.

What is the contrapositive of a false statement?

Contrapositive of a false statement is also false. The conditional statement and its contrapositive are logically equivalent. Contrapositive is used when an implication has many hypotheses or when the hypothesis specifies infinitely many objects.