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Given Set = (-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36).

Determine which of the following statements are true and which are false. For each statement that is true, enter TRUE. For each statement that is false, enter a case that could be used to show the statement is false.

(a) If x is odd, then x > 0.

User Plspl
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1 Answer

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Final answer:

The statement 'If x is odd, then x > 0' when considering the set provided is false, as it does not hold true for the number '23', which is an odd number greater than 0. The corrected statement should acknowledge that an odd number can be greater than 0.

Step-by-step explanation:

The student's question is asking whether the following statement is true or false: If x is odd, then x > 0. We need to examine the elements of the set provided to determine if the statement holds true for all odd numbers within the set.

Looking at the set (-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36), we can see that there is an odd number, specifically '1' and '3', which are greater than 0. However, '23' is also odd, but it is greater than 0 as well. Therefore, the statement is FALSE. To provide a counterexample, we could show that although '23' is an odd number, it is not less than or equal to 0; thus, the statement does not hold in general.

Corrected statement: If x is an odd number in the set, then x can be greater than 0.

User Jie
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