Let \(A = \{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5\}\), \(B = \{1, 2, 3, 4, 5\}\), \(C = \{1\}\), \(D = \{1, \{1\}\}\) S1 : A and B are equal S2 : C and D are equal then .................... is True
S1 and ~S2
Rule: two sets are equal when they have exactly the same distinct elements; repetition and order do not matter.
Distinct elements of A: \(\{1, 2, 3, 4, 5\} = B\), so S1 is true.
\(C = \{1\}\) has one element; \(D = \{1, \{1\}\}\) has two elements, \(1\) and the set \(\{1\}\).
\(\{1\} \in D\) but \(\{1\} \notin C\), so \(C \ne D\) and S2 is false, i.e. ~S2 is true.
Combining: S1 is true and ~S2 is true.
Hence, S1 and ~S2.
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