In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

Question

CASE_STUDIESSubset of a Set6 sub-questions

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Consider the sets φ, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol ⊂ or ⊄ between each of the following pair of sets:

Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No. (Why?). Is B a subset of A? No. (Why?)

Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :

Examine whether the following statements are true or false:

Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?