3. Suppose e and f are real numbers where e>0 and f<0.

(a) Is - e+f positive or negative. Explain how you know.

(b) Is e-f positive or negative? Explain how you know.

(c) Is f-e positive or negative. Explain how you know.

Part A:

Given that e and f are real numbers where e > 0 and f < 0.

Since e > 0, this means that e is positive and - e is negative.

Also, since f < 0, this means that f is negative.

The sum of two negative numbers gives a negative number.

Therefore, - e + f is negative.

Part B:

Given that e and f are real numbers where e > 0 and f < 0.

Since e > 0, this means that e is positive.

Also, since f < 0, this means that f is negative and - f is positive.

Recall that e - f = e + (-f)

The sum of two positive numbers gives a positive number.

Therefore, e - f is positive.

Part C:

Given that e and f are real numbers where e > 0 and f < 0.

Since e > 0, this means that e is positive and - e is negative.

Also, since f < 0, this means that f is negative.

Recall that f - e = f + (-e)

The sum of two negative numbers gives a negative number.

Therefore, f - e is negative.