Question

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
(i) $A\cup B$
(ii) $A\cup C$
(iii) $B\cup C$
(iv) $B\cup D$
(v) $A\cup B\cup C$
(vi) $A\cup B\cup D$
(vii) $B\cup C\cup D$
(viii) $A\cap \left(B\cup C\right)$
(ix) $\left(A\cap B\right)\cap \left(B\cap C\right)$
(x) $\left(A\cup D\right)\cap \left(B\cup C\right)$.

Answer 1

Given:
A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}
(i) $A\cup B$ = {1, 2, 3, 4, 5, 6, 7, 8}
(ii) $A\cup C$ = {1, 2, 3, 4, 5, 7, 8, 9, 10, 11}
(iii) $B\cup C$ = {4, 5, 6, 7, 8, 9, 10, 11}
(iv) $B\cup D$ = {4, 5, 6, 7, 8, 10, 11, 12, 13, 14}
(v) $A\cup B\cup C$ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
(vi) $A\cup B\cup D$ = {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14}
(vii) $B\cup C\cup D$ = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
(viii) $A\cap \left(B\cup C\right)$ = {4, 5}
(ix) $\left(A\cap B\right)\cap \left(B\cap C\right)$ = $\mathrm{\varphi }$
(x) $\left(A\cup D\right)\cap \left(B\cup C\right)$ = {4, 5, 10, 11}