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Which of the following statements has a false contrapositive and a true converse?

a) If the product of two numbers is zero, then at least one of the numbers is zero.
b) If the product of two numbers is even, then both numbers are even.
c) If a triangle is right angled, then it contains two acute angles.
d) If a rectangle has two equal adjacent sides , then it is a square.
e) If an egg is boiled for 18 minutes, then it is hard boiled.

2007-06-05 11:12:15 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

b. The converse of this statement is "if two numbers are both even, then their product is even," which is true, but the contrapositive is "If two numbers are not both even, then their product is not even," which has the trivial counterexample 2*1.

2007-06-05 11:18:07 · answer #1 · answered by Pascal 7 · 1 0

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