This would be logically equivalent to the conditional you started with.
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.
The original statement is: "If a triangle has three sides of the same length, then it is equilateral." Inverse: "If a triangle does not have three sides of the same length, then it is not equilateral." Converse: "If a triangle is equilateral, then it has three sides of the same length." Contrapositive: "If a triangle is not equilateral, then it does not have three sides of the same length."
The statement "If p, then q; and if q, then r; therefore, if p, then r" is an example of a syllogism, specifically a form of logical reasoning known as the transitive property. The converse of this statement would be "If r, then p," which is not necessarily true based on the original premises. The contrapositive would be "If not r, then not p," and the inverse would be "If not p, then not q."
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
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conditional and contrapositive + converse and inverse
conditional and contrapositive + converse and inverse
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.
The second statement is the contrapositive of the first. The contrapositive of a statement reverses and negates both the hypothesis and conclusion. In logical terms, if the first statement is "If P, then Q," the contrapositive is "If not Q, then not P."