In logic, which of the following is said to be logically equivalent to the original statement?
a.) converse
b.) inverse
c.) negation
d.)contrapositive
To determine which of the options is logically equivalent to the original statement, let's go through each option and explain what they mean:
a.) Converse: The converse of a statement is formed by interchanging the hypothesis and conclusion of the original statement. In other words, if the original statement is "If P, then Q," the converse would be "If Q, then P."
b.) Inverse: The inverse of a statement is formed by negating both the hypothesis and the conclusion of the original statement. So, if the original statement is "If P, then Q," the inverse would be "If not P, then not Q."
c.) Negation: Negation is a term used to describe the opposite of a statement. In logic, the negation of a statement is formed by adding "not" to the original statement. So, if the original statement is "P," the negation would be "not P."
d.) Contrapositive: The contrapositive of a statement is formed by both negating the hypothesis and the conclusion of the original statement, and then interchanging them. If the original statement is "If P, then Q," the contrapositive would be "If not Q, then not P."
Now, to find the option that is logically equivalent to the original statement, we need to look for the one that has the same truth value as the original statement.
In this case, the option that is logically equivalent to the original statement is d.) Contrapositive. The contrapositive of a statement is always logically equivalent to the original statement.