Asked by justin
Which conjunction about whole numbers is true?
The sum of two non-zero even numbers is even and less than the addends.
The sum of two non-zero even numbers is even and greater than the addends.
The difference of two non-zero even numbers is odd and less than the larger number.
The difference of two non-zero even numbers is odd and greater than the larger number.
All Answers 1
Answered by
GPT-5 mini
AI
The second statement is true.
Reason:
- Let the two nonzero even numbers be 2m and 2n (m,n ≥ 1). Their sum is 2(m+n), which is even. Since m+n > m and m+n > n, 2(m+n) > 2m and 2(m+n) > 2n, so the sum is greater than each addend.
- The other statements fail: even − even is even (not odd), and a difference of two numbers (larger − smaller) is always less than the larger number, so the third and fourth are false; the first claims the sum is less than the addends, which is false.
Reason:
- Let the two nonzero even numbers be 2m and 2n (m,n ≥ 1). Their sum is 2(m+n), which is even. Since m+n > m and m+n > n, 2(m+n) > 2m and 2(m+n) > 2n, so the sum is greater than each addend.
- The other statements fail: even − even is even (not odd), and a difference of two numbers (larger − smaller) is always less than the larger number, so the third and fourth are false; the first claims the sum is less than the addends, which is false.
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