Question

A(1,3,5, 7,9}, B {0,1,2,3,4,5,6, 7,8,9} be the universal set and let A (0,2,4,6,8}, and C {2,3,5,7}. List the elements of the following sets 1.) Let U (a) An B (b) C\B (c) AU (Bnc)

Answer 1

a)
`A \cap B = \{\phi\}`

b)
`\{0, 2, 3, 4, 5,6, 7, 8\}`

c)
`\{0, 2, 3, 4, 5,6, 7, 8\}`

Explanation:

We are given the following information:

The universal set is : U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {0, 2, 4, 6, 8}

B = {1, 3, 5, 7, 9}

C = {2, 3, 5, 7}

a)
`A \cap B = \{\phi\}`

b)
`C/B = C \cap \overline{B} = \{2, 3, 5, 7\} \cap \{0, 2, 4, 6, 8\} = \{2\}`

c)

`A \cup (B \cap C) = \{0, 2, 4, 6, 8\} \cup (\{1, 3, 5, 7, 9\} \cap \{2, 3, 5, 7\})\\=\{0, 2, 4, 6, 8\} \cup \{3, 5, 7\}\\= \{0, 2, 3, 4, 5,6, 7, 8\}`