Question

A subset A, Band C of the universal set U = {x: 6 ≤ x ≤ 40} are defined as follows: A = {x: x is a prime number}, B = {x: x² is less than 36} and C = { x:x EU and x # A}. List the elements of the above sets​

Answer 1

Explanation:

The universal set U is the set of integers between 6 and 40, inclusive.

A = {x: x is a prime number}

The prime numbers between 6 and 40 are:

A = {7, 11, 13, 17, 19, 23, 29, 31, 37}

B = {x: x² is less than 36}

The squares of the integers between 0 and 6 are:

0² = 0

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

So B consists of the integers whose squares are less than 36:

B = {0, 1, 2, 3, 4, 5}

C = { x: x EU and x # A}

C consists of the integers in U that are not in A:

C = {6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40}

So the elements of A, B, and C are:

A = {7, 11, 13, 17, 19, 23, 29, 31, 37}

B = {0, 1, 2, 3, 4, 5}

C = {6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40}