Consider the statement:
If two whole numbers are even, then their sum is odd.
What assumption should be made to prove the statement indirectly?
A- The numbers are equal.
B- The numbers are not equal.
C- Their sum is not odd.
D- Their difference is even.
My choice is C.
Yes, C is the correct answer.
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To prove the statement indirectly, you need to assume the negation of the statement and derive a contradiction.
The negation of the statement "If two whole numbers are even, then their sum is odd" is "There exist two whole numbers that are even, and their sum is not odd."
Therefore, you assume that there exist two whole numbers, let's say 'a' and 'b', that are even and their sum is not odd.
To derive a contradiction, you would need to show that this assumption leads to a contradiction. In this case, the contradiction would be that the sum of two even numbers is indeed odd.
Out of the given options, your choice (C) "Their sum is not odd" aligns with the assumption needed to prove the statement indirectly.