Discussion
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
Answer: D
The answer is S1 and ~S2: S1 is true and S2 is false.
A set is determined only by which elements it contains; repetition and order are ignored. Listing 2 twice or 5 five times in A adds nothing, so A = {1, 2, 3, 4, 5} = B, and S1 is true.
C = {1} has one element. D = {1, {1}} has two: the number 1 and the set {1}. Since {1} is an element of D but not of C, the sets differ and S2 is false. So the true combination is S1 and the negation of S2, which rules out the other three options.
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