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☼ Complement of a Set : Let A be a subset of the universal set U, then the complement of A, denoted by Aٰ or A is defined by :
Aٰ = A = { x : x U, x A }.
Clearly, x A x A.
e.g.
☼ Universal Set : In the discussion about sets, all sets are assumed to be the subsets of a definite set. This definite set is called the universal set. Universal set contains the sets under discussion as subsets. The symbol U i…
☼ Intersection of Sets : The intersection of two sets A and B, denoted by A B is the set of all those elements which are common to both A and B.
Thus, A
☼ Equivalent Sets : Two sets A and B are said to be equivalent if n (A) = n (B).
■ Remark : Equivalent sets are not always equal but equal sets are always equivalent. Thus, { 10, 20…