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Subjective Type

Let $$U=\{1,2,3,4,5,6,7,8,9\},A=\{1,2,3,4\},B=\{2,4,6,8\}$$ and $$C=\{3,4,5,6\}$$. Find (i) $$A^{\prime }$$ (ii) $$B^{\prime }$$ (iii) $$(A\cup C{)}^{\prime }$$ (iv) $$(A\cup B{)}^{\prime }$$ (v) $$(A^{\prime }{)}^{\prime }$$ (vi) $$(B-C{)}^{\prime }$$

Solution

$$U=\{1,2,3,4,5,6,7,8,9\}$$
$$A=\{1,2,3,4\}$$
$$B=\{2,4,6,8\}$$
$$C=\{3,4,5,6\}$$

(i) $$A^{\prime }=U-A=\{5,6,7,8,9\}$$

(ii) $$B^{\prime }=\{1,3,5,7,9\}$$

(iii) $$A\cup C=\{1,2,3,4,5,6\}$$
$$\therefore (A\cup C{)}^{\prime }=\{7,8,9\}$$

(iv) $$A\cup B=\{1,2,3,4,6,8\}$$
$$(A\cup B{)}^{\prime }=\{5,7,9\}$$

(v) We know $$(A^{\prime }{)}^{\prime }=A$$
$$\Rightarrow (A^{\prime }{)}^{\prime }=\{1,2,3,4\}$$

(vi) $$B-C=\{2,8\}$$
$$\therefore (B-C{)}^{\prime }=\{1,3,4,5,6,7,9\}$$

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