Q: What is the inverse of the contrapositive of the converse?

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if the statement is : if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not

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No, the inverse is not the negation of the converse. Actually, that is contrapositive you are referring to. The inverse is the negation of the conditional statement. For instance:P → Q~P → ~Q where ~ is the negation symbol of the sentence symbols.

First, it helps to look at the verb usage: you can reverse something, but you cannot inverse or converse something.The distinctions between reverse, converse, and inverse can often be made by looking at their roots and simple forms.Reverse - look at revert. It means to return to a former condition, position, etc. The root is from the Latin reversus, which means to turn back. Reverse is often used to describe a directional change."I reversed my position on the matter.""The water is now flowing in reverse."Converse - look at convert. It means to change from one form to another. The root is from the Latin converses, which means to turn around. Converse is often used to describe the 'exact' opposite."Black is the converse color of white.""Jill is a democrat; conversely, Jack is a republican."Inverse - look at invert. It means to turn upside down or inside out. The Latin root, inversus, means the same. Inverse is often used to compare how two things are related in an opposite matter."The inverse of 1,2,3,4 is 4,3,2,1." *note that reverse is a process of inversion"The relationship between the amounts of water in a container is inverse to the amount of space; the amount of space decreases as the amount of water increases." *note that the reverse of this is not trueWhen used in logical or mathematical statements:If the statement is: if p then q* converse: if q then p* inverse: if not p then not q* contrapositive: if not q then not pIf a statement is true, the contrapositive is also logically true. Likewise, when the converse is true, the inverse is also logically true.

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Related questions

The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.

if the statement is : if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not

The inverse of a conditional statement switches the hypothesis and conclusion. The converse of a conditional statement switches the hypothesis and conclusion. The contrapositive of a conditional statement switches and negates the hypothesis and conclusion.

conditional and contrapositive + converse and inverse

conditional and contrapositive + converse and inverse

conditional and contrapositive + converse and inverse

conditional and contrapositive + converse and inverse

none

No, the inverse is not the negation of the converse. Actually, that is contrapositive you are referring to. The inverse is the negation of the conditional statement. For instance:P → Q~P → ~Q where ~ is the negation symbol of the sentence symbols.

if then form: if you can do it, then we can help converse: if we help, then you can do it. inverse: if you cant do it, then we cant help contrapositive: if we cant help, then you cant do it.

A conditional statement is true if, and only if, its contrapositive is true.

Conditional statements are also called "if-then" statements.One example: "If it snows, then they cancel school."The converse of that statement is "If they cancel school, then it snows."The inverse of that statement is "If it does not snow, then they do not cancel school.The contrapositive combines the two: "If they do not cancel school, then it does not snow."In mathematics:Statement: If p, then q.Converse: If q, then p.Inverse: If not p, then not q.Contrapositive: If not q, then not p.If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.