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## Main Question or Discussion Point

I am currently covering Set Theory from the book, A Transition to Abstract Mathematics (Douglas Smith) and have a question about subsets and an implication. The statement reads as follows:

If B is a subset of A, then {B} is an element of the Power Set A.

I choose this to be true. By definition the Power Set A is comprised of all subsets of A. Given the first condition that B is a subset of A I can't really see how this is false, which the book gives as the correct answer. Does it have something to do with the braces around B? The way I interpreted the statement is: If B is a subset of A, then the set B is an element of the Power Set A. I know, for example, that when x is an element of A this does not automatically imply it is also an element of the Power Set A, this is one of the cases from which the confusion arises. Thanks in advance.

Joe

If B is a subset of A, then {B} is an element of the Power Set A.

I choose this to be true. By definition the Power Set A is comprised of all subsets of A. Given the first condition that B is a subset of A I can't really see how this is false, which the book gives as the correct answer. Does it have something to do with the braces around B? The way I interpreted the statement is: If B is a subset of A, then the set B is an element of the Power Set A. I know, for example, that when x is an element of A this does not automatically imply it is also an element of the Power Set A, this is one of the cases from which the confusion arises. Thanks in advance.

Joe