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Question

A={1.2} ,B={{1},{2}} C={{1},{1,2}}

is

A=B

A is into B

A belong to C

A is into C

Answer 1

Hi Hamza,

This is a problem where you have to be very careful with the definitions. Let us rule out each of the wrong options:

1. A = B is WRONG, because A and B do not have the same elements. For example, 1 is an element of A, but not an element of B (note that {1} is an element of B, but 1 is not an element of B).
2. A is a subset of B is WRONG, because A has elements that B does not. As in the previous bullet point, 1 is an example of an element of A that is not an element of B.
3. A is a subset of C is WRONG, because A has elements that C does not. Just as with B, we observe that 1 is not an element of C, even though {1} is an element of C.

That leaves A is an element of C as the only possible correct answer. And we can check that it is valid. The set C has two elements in it. One of them is {1} and the other is {1, 2}. This latter one, {1, 2}, is exactly A. So A is one of the two elements of C.

I hope this is helpful --- please feel free to contact me for help in the future.