What is the logical equivalent of the converse of the contrapositive of a conditional statement?

conditional
contrapositive
reverse
inverse

Let P and Q be any two logical statements. A logical statement is a sentence in which it is either true or false. An example of a logical statement would be "the door is open" because the door is either open or closed (making the statement true or false). A non-example would be "who is that person?" because there is no true or false status of the statement.

A conditional statement is of the form "If P, then Q". We can use shorthand notation to write "P --> Q" showing a direction of cause and effect. Statement P connects to Q, or statement P causes statement Q to happen.

The converse is where we swap P and Q to get Q --> P

The inverse is where we negate P and Q of the original conditional to get ~P --> ~Q. The tilde means "not". Writing "~P" is shorthand for "not P". For example, if P = it has rained, then ~P = it has not rained.

The contrapositive is where we do both the inverse and converse at the same time. Basically we swap P and Q of the original conditional, and we negate both P and Q as well. The contrapositive would be ~Q --> ~P

To summarize so far

Original Conditional: P --> Q

Converse: Q --> P

Inverse: ~P --> ~Q

Contrapositive: ~Q --> ~P

If we apply the converse operation to the contrapositive, then this is just a fancy way of saying "swap the positions of ~Q and ~P". This means we go from ~Q --> ~P to ~P --> ~Q.

Therefore the converse of the contrapositive is the inverse.

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step-by-step explanation: