Question

Select the correct answer. a number is selected at random from the set {2, 3, 4, ... 10}. which event, by definition, covers the entire sample space of this experiment? a. the number is even or less than 12. b. the number is neither prime nor composite. c. the number is greater than 2. d. the number is not divisible by 5.

Answer 1

Answer: answer above me is correct

Answer 2

a. the number is even or less than 12

Explanation:

why ?

let's look at the logic of the statements :

a.

the number is even

true for 2, 4, 6, 8, 10

false for 3, 5, 7, 9

so, false in general.

but there is an "or" condition, which makes the true/false status of the first condition irrelevant, as false or true is always true, and false or false is always false.

and this "or" condition says "less than 12". that is true for all given numbers.

so, false or true = true is or result here.

b.

"neither prime nor composite" means "not prime and not composite". what else would there be ? this could only be true for an empty set of numbers. so, it is false here.

c.

"the number is greater than 2" is false for 2 and therefore false for the entire sample space (even though it is true for most of the numbers. but it is not true for all).

d.

"the number is not divisible by 5" is false for 5 and 10.

so, the same principles of c. apply.