If a polygon is a triangle, then it has 3 sides. If I am not standing in United Kingdom, then I am not standing in Manchester. If am standing in Manchester, then I am standing in United Kingdom. If sin(x) is not zero, then x is not zero. 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.
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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. Contrapositive Statement Characteristicsĭefinition: 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”.