The Universal \xi = {multiples of 3 less than 30} A = {odd numbers} B = {numbers greater than 15} A and B are subsets of the universal set. Find the value of: n(A \cap B')

remolatg 2021-08-02 Answered
The Universal \(\displaystyle\xi=\) {multiples of 3 less than 30}
\(\displaystyle{A}=\) {odd numbers}
\(\displaystyle{B}=\) {numbers greater than 15}
A and B are subsets of the universal set.
(a). List the members of: (i). \(\displaystyle\xi\)
(ii). A
(iii) B
(b). List the members of:
(i). \(\displaystyle{A}\cup{B}\)
(ii). \(\displaystyle{A}\cap{B}\)
(iii). \(\displaystyle{A}'\cap{B}\)
(c). List the members of: \(\displaystyle{\left({A}\cup{B}'\right)}\cap{A}'\)
(d). Find the value of: \(\displaystyle{n}{\left({A}\cap{B}'\right)}\)

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Expert Answer

Obiajulu
Answered 2021-08-03 Author has 24220 answers

Step 1
Here a universal set and two subsets are given.
We have to find the following members in the each relation.
Step 2
a) The universal \(\displaystyle\xi=\) {multiples of 3 less than 30}
\(\xi = \{3,6,9,12,15,18,21,24,27\} \)
A and B are subset of the universal set \(\displaystyle\xi\)
\(\displaystyle{A}=\) {add numbers}
\(A = \left\{3,9,15,21,27\right\}\)
\(\displaystyle{B}=\) {numbers greater than 15}
\(\displaystyle{B}=\{{18},{21},{24},{27}\}\)
i) \(\displaystyle\xi=\{{3},{6},{9},{12},{15},{18},{21},{24},{27}\}\)
ii) \(\displaystyle{A}=\{{3},{9},{15},{21},{27}\}\)
iii) \(\displaystyle{B}=\{{18},{21},{24},{27}\}\)
Step 3
b) i) \(\displaystyle{A}\cup{B}\{{3},{9},{15},{18},{21},{24},{27}\}\)
ii) \(\displaystyle{A}\cap{B}=\{{21},{27}\}\)
\(\displaystyle{A}'=\{{6},{12},{18},{24}\}\)
iii) \(\displaystyle{\left({A}'\cap{B}\right)}=\{{18},{24}\}={A}'\cap{B}\)
c) \(\displaystyle{B}'=\{{3},{6},{9},{12},{15}\}\)
\(\displaystyle{A}\cup{B}'=\{{3},{6},{9},{12},{15},{21},{27}\}\)
\(\displaystyle{\left({A}\cup{B}'\right)}\cap{A}'=\{{6},{12}\}\)
d) \(\displaystyle{A}\cap{B}'=\{{3},{9},{15}\}\)
\(\displaystyle{n}{\left({A}\cap{B}'\right)}={3}\)

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