If \( a > 0 \) and \( b < 0 \), then which of the following must be true?

A. \( ab > 0 \)

B. \( a + b < 0 \)

C. \( a - b > 0 \)

D. \( a + b > 0 \)

E. \( b - a > 0 \)

We need to find the correct answer on the given choices:
If a > 0 and b < 0, then The answer is a + b > 0
let’s give a specific example:
let’s have a = 1
and b = .20


Now, let’s try calculating if our answer is correct.
Thus a + b > 0
=> a + b
=> 1 + .20
=> 1.20
and 1.20 is greater than 0.
=>Therefore 1.20 > 0 = a + b > 0

Answered by taskmasters | 2024-06-10

The statement that must be true if a > 0 and b < 0 is that a - b > 0, as subtracting a negative number is identical to adding its positive counterpart, increasing the value of a. ;

Answered by utkarshsingh1281 | 2024-06-24

The only true statement from the options provided is C: 0"> a − b > 0 , as subtracting a negative b from a positive a results in a positive value. All other options do not hold true under the given conditions. Thus, Option C is chosen as the correct answer.
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Answered by taskmasters | 2025-03-07