Find a counterexample to show that each statement is false. The sum of any three odd numbers is even. When an even number is added to the product of two odd numbers, the result will be even. When an odd number is squared and divided by 2, the result will be a whole number.

Tazmin Horton

Tazmin Horton

Answered question

2021-06-03

Find a counterexample to show that each statement is false.
The sum of any three odd numbers is even.
When an even number is added to the product of two odd numbers, the result will be even.
When an odd number is squared and divided by 2, the result will be a whole number.

Answer & Explanation

Jayden-James Duffy

Jayden-James Duffy

Skilled2021-06-04Added 91 answers

Any three odd integers added together equal even.
1 + 3 + 5 = 9, where 1, 3, and 5 are all odd numbers but their addition, 9, is also odd, could serve as a counterexample.
The outcome will be even if an even number is added to the product of two odd numbers.
A possible counterexample is (3×5)+2=1 where the product of 3 and 5 is 15 (odd) but when 2 (even) is added, the result is 17 which is odd.
A whole number is produced when an odd number is squared and divided by 2.
A possible counterexample is 522=12.5 where 5 is odd and when squared and divided by 2, the result is not a whole number.

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