Consider the following statements: I. If A is a subset of U and U is the Universal set, then the complement of the set A is also a subset of U. II. The complement of a Universal set is a singleton set. Which of the statements given above is/are correct?
I only
Statement I is correct because the complement of \(A\), defined as \(A'=U-A\), always consists of elements of \(U\) and so is a subset of \(U\). Statement II is incorrect because the complement of the Universal set is \(U-U=\varnothing\), the empty set, not a singleton set. Hence only statement I is correct.
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Important Questions from Operations on Sets
Match List I with List II
Let R 1= {(1, 1), (2, 2), (3, 3)} and R 2 = {(1, 1), (1, 2), (1, 3), (1, 4)}
List I
List II
(A) R 1∪ R 2
(I) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (3, 3)}
(B) R 1- R 2
(II) {1, 1}
(C) R 1∩ R 2
(III) {(1, 2), (1, 3), (1, 4)}
(D) R 2- R 1
(IV) {(2, 2), (3, 3)}
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