Question

Sets A and B are subsets of the universal set U.These sets are defined as follows.U={k, m, q.7.x, 2)A ={k, g)B={m,q)Find the following sets.Write your answer in roster form or as Ø.(a) ANB' = 00,0....(b) (AUB)' = 0Х5?

Answer 1

ANSWER :

a. {2, 6, 9}

b. {6}

EXPLANATION :

From the problem, we have the sets :

$\begin{gathered} U=\lbrace2,3,4,6,9\rbrace \\ A=\lbrace2,3,4\rbrace \\ B=\lbrace3,4,6\rbrace \end{gathered}$

A' denotes the elements that are NOT present in A but present in U.

B' denotes the elements that are NOT present in B but present in U.

That will be :

$\begin{gathered} A^{\prime}=\lbrace6,9\rbrace \\ B^{\prime}=\lbrace2,9\rbrace \end{gathered}$

a. A' ∪ B'

The symbol ∪ denotes the union of two sets.

That will be :

$A^{\prime}\cup B^{\prime}=\lbrace2,6,9\rbrace$

b. A' ∩ B

The symbol ∩ denotes the intersection or common elements of the two sets

That will be :

$A^{\prime}\cap B^=\lbrace6\rbrace$