Question

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {1, 2, 3, 5, 7}, and C = {1, 3, 6, 7}.Find (A U B)’Question 44 options:a) { }b) {1, 2, 3, 4, 5, 6, 7}c) {2, 4, 6}d) {2}

Answer 1

Answer: $(AUB)^{\prime}\text{ = \textbraceleft \textbraceright \lparen option A\rparen}$Explanation:

Given:

U = {1, 2, 3, 4, 5, 6, 7}

A = {2, 4, 6}

B = {1, 2, 3, 5, 7}

C = {1, 3, 6, 7}

To find:

(A U B)’

First, we will find (A U B):

A = {2, 4, 6}

B = {1, 2, 3, 5, 7}

$\begin{gathered} (A\text{ U}B):all\text{ the numbers in A and B without repetition} \\ \left(AUB\right)=\text{ \textbraceleft}{2,4,6,1,2,3,5,7}\rbrace \\ (AUB)={\text{ \textbraceleft}1,2,2,3,4,5,6,7\rbrace} \\ without\text{ repeating the numbers:} \\ (A\text{ U B\rparen= \textbraceleft1, 2, 3, 4, 5, 6, 7\textbraceright} \end{gathered}$$\begin{gathered} (A\text{ U}B)^{\prime}\text{ : this entails the numbers that are in U }but\text{ not in \lparen A U}B) \\ U\text{ = \textbraceleft1, 2, 3, 4, 5, 6, 7\textbraceright} \\ (AUB)=\left\{1,2,3,4,5,6,7\right\} \\ The\text{ numbers in both sets are the same} \\ \\ Hence,\text{ the complement of \lparen AUB\rparen will be a null set} \\ (AUB)^{\prime}\text{ = \textbraceleft \textbraceright \lparen option A\rparen} \end{gathered}$