Question

Suppose A = {2, 5, 7, 9, 13, 25, 26}.

(a) Find n(A).

(b) True or false: 13 ∈ A

(c) True or false: 26 ∉ A

(d) True or false: 10 ∉ A

Answer 1

n(A) is the number of elements is A, sometimes written |A|. I count 7. n(A)=7

13 is among the elements of A, so 13 ∈ A is TRUE

26 is among the elements of A, so 26 ∉ A is FALSE

10 isn't in A, so 10 ∉ A is TRUE

Answer 2

(a) 7

(b) TRUE

(c) FALSE

(d) TRUE

Explanation:

In part (a), we are asked for n(A), the number of elements is A.

We count them and we get that set A hast 7 elements.

Then, n(A) = 7

In part (b), we are asked if 13 is an element of the set A.

We go over each element of A and check that 13 is there, hence 13 ∈ A.

Then, the statement "13 ∈ A" is TRUE

In part (c), we are asked if 26 is not an element of the set A.

We go over each element of A and check that 26 is there, hence 26 ∈ A.

Then, the statement "26 ∉ A" is FALSE.

In part (d), we are asked if 10 is not an element of the set A.

We go over each element of A and check that 10 is not there, hence 10 ∉ A.

Then, the statement "10 ∉ A" is TRUE.