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Converse geometry examples9/9/2023 ![]() ![]() If x is equal to zero, then sin(x) is equal to zero. If all the four sides are not equal then it is not a square. If a figure is a square then all the four sides are equal. If the grass is not wet then it is not raining. ‘If q then p’ is a contrapositive of the conditional statement ‘if p then q’.Ĭontrapositive of a conditional statement is logically equivalent to its conditional statement. The inverse statement is obtained by negating both hypothesis and conclusion. The conclusion q of the conditional statement becomes the hypothesis of the converse. The hypothesis p of the conditional statement becomes the conclusion of the converse. The contrapositive of a conditional statement is a combination of the converse and inverse. ![]() If the conditional of a statement is p q then, we can compose the contrapositive statement by interchanging the hypothesis and conclusion of the inverse of the same conditional statement. Contrapositive can be used as a strong tool for proving mathematical theorems because contrapositive of a statement always has the same truth table.Contrapositive is used when an implication has many hypotheses or when the hypothesis specifies infinitely many objects.The conditional statement and its contrapositive are logically equivalent. Contrapositive of a false statement is also false.Contrapositive of a true statement is also true.The contrapositive of any true proposition is also true.A conditional statement is in the form “If p, then q” where p is the hypothesis while q is the conclusion.Ĭontrapositive Statement C haracteristics The contrapositive of a conditional statement is a combination of the converse and inverse.Ĭonditional statement: A conditional statement also known as an implication. Definition: Contrapositive is exchanging the hypothesis and conclusion of a conditional statement and negating both hypothesis and conclusion.įor example the contrapositive of “if A then B” is “if not-B then not-A”. ![]()
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