Question

If I wanted to ask someone a question about income and my question looks like this:

Which category best describes your annual income?

a. $1-$20,000

b. $20,000-$40,000

c. $40,000-$60,000

d. $60,000-$80,000

Could you say that my answer choices are exhaustive and mutually exclusive? If not, why not? What would my answers need to look like?

Answer 1

We cannot say that answer choices are exhaustive and mutually exclusive

REASON:

(i) Not exhaustive: $0 is not covered. i.e., a person with nil income is not included. Also, a person with greater than $80,000 is not covered.

(ii) Not mutually exclusive: $20,000 occurs in (a) & (b). $40,000 occurs in (b) & (c) etc.

The category best describes annual income:
(a) $0 up to & not including $20,000

(b) $20,000 up to & not including $40,000

(c) $40,000 up to & not including $60,000

(d) $60,000 up to & not including $80,000

(e) above $80,000