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Write the converse of the conditional statement. If the converse is false, provide a counterexample. 21. If two angles are not adjacent, then they are vertical angles. 22. If x is odd, then 3x is odd. ODD OOD uec.se Write the inverse of the conditional statement. 23. If an angle measures 300, then it is acute. IF TYE OF IS 300 A-COTE 24.

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There we learned the four variations of a proposition: the obverse (the proposition itself), the inverse, the converse, and the contrapositive. Obverse: If P then Q. Inverse: If not P then not Q. Converse: If Q then P. Contrapositive: If not Q then not P. If the obverse is true, then the contrapositive is also true. The inverse and converse may not be. Mathematical reasoning is a deductive process and the basic entity to it is a statement. The statements in reasoning can be compound i.e. they can be composed of two or more than two statements together.

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The inverse of a conditional is the contrapositive of the converse. The converse of "If A then B" is "If B then A"; the contrapositive of "If B then A" is "If ~A then ~B". While the contrapositive does necessarily follow , the converse does not. So inferring the inverse from a conditional alone is an invalid argument. Thus the argument is ...

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