Question 33 of 47beginner🔧 ApplyShort Answer2 marks

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:

(i)

A = {a, b, c}

Answer

The complement of set A consists of elements in the universal set U that are not in A. Given U={a,b,c,d,e,f,g,h}U = \{a, b, c, d, e, f, g, h\} and A={a,b,c}A = \{a, b, c\}, the elements not in A are d, e, f, g, h. Therefore, A′={d,e,f,g,h}A' = \{d, e, f, g, h\}.

(ii)

B = {d, e, f, g}

Answer

For set B={d,e,f,g}B = \{d, e, f, g\}, the elements in U that do not belong to B are a, b, c, h. Therefore, the complement B′={a,b,c,h}B' = \{a, b, c, h\}.

(iii)

C = {a, c, e, g}

Answer

For set C={a,c,e,g}C = \{a, c, e, g\}, the elements in U that do not belong to C are b, d, f, h. Therefore, the complement C′={b,d,f,h}C' = \{b, d, f, h\}.

(iv)

D = {f, g, h, a}

Answer

For set D={f,g,h,a}D = \{f, g, h, a\}, the elements in U that do not belong to D are b, c, d, e. Therefore, the complement D′={b,c,d,e}D' = \{b, c, d, e\}.

Explanation

The solution applies the definition of the complement of a set as demonstrated in Example 20 of the provided text. The complement of a set A, denoted by A', contains all elements of the universal set U that are not present in set A. By identifying the elements present in U but missing from each specific set (A, B, C, D), we determine their respective complements.

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