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Let A = {2,{4,5},4}. Which of the following statements are incorrect and why? Give an explanation for your answer to each part.

i. 5 ∈ A?
ii. {5} ∈ A?
iii. 5 ⊂ A?

2 answers

Let C = {4,5}

Then A = {2,C,4}

They are all incorrect, and it should be clear why. What are your reasons?
If C={4,5} then {4,5} is treated as one element comprised of the separate elements 4 and 5 . Therefore, 5 itself is not an element of A . Thus, {5} cannot be an element of A. 5 is not a subset of A because it is a part of the pair of elements in C.