Question

If A = {1, 2, 3, 4}, B{3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; 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) $B\cup C\cup D$

Answer 1

Here A = {1, 2, 3, 4}, B = {3, 4, 5, 6},

C = {5, 6, 7, 8} and D = {7, 8, 9, 10}

(i) $A\cup B$ = {1, 2, 3, 4} $\cup$ {3, 4, 5, 6}

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

(ii) $A\cup C$ = {1, 2, 3, 4} $\cup$ {5, 6, 7, 8}

= {1, 2, 3, 4, 5, 6, 7, 8}

(iii) $B\cup C$ = {3, 4, 5, 6} $\cup$ {5, 6, 7, 8}

= {3, 4, 5, 6, 7, 8}

(iv) $B\cup D$ = {3, 4, 5, 6} $\cup$ {7, 8, 9, 10}

= {3, 4, 5, 6, 7, 8, 9, 10}

(v) $A\cup B\cup C$

= {1, 2, 3, 4} $\cup$ {3, 4, 5, 6} $\cup$ {5, 6, 7, 8}

= {1, 2, 3, 4, 5, 6} $\cup$ {5, 6, 7, 8}

= {1, 2, 3, 4, 5, 6, 7, 8}

(vi) $A\cup B\cup D$

= {1, 2, 3, 4} $\cup$ {3, 4, 5, 6} $\cup$ {7, 8, 9, 10}

= { 1, 2, 3, 4, 5, 6} $\cup$ {7, 8, 9, 10}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(vii) $B\cup C\cup D$

= {3, 4, 5, 6} $\cup$ {5, 6, 7, 8} $\cup$ {7, 8, 9, 10}

= {3, 4, 5, 6, 7, 8} $\cup$ {7, 8, 9, 10}

= {3, 4, 5, 6, 7, 8, 9, 10}