Given a set in Description below, answer the following questions.

Question

1. Is A ⊆ B?
2. Is B ⊆ A?
3. Is either A or B a proper subset of the other?

Answer 1

The first thing you’ll want to do for questions like these is make sure you’ve got a good understanding of the definitions of the relevant concepts: subset and proper subset.

X is a subset of Y if and only if all elements of X are elements of Y.

X is a proper subset of Y if and only if X is a subset of Y and X ≠ Y.

Different texts may phrase these definitions is slightly different ways (e.g., in terms of “membership”), but the concepts are likely to be very similar.

What makes your question a little more challenging is that some of the elements of the sets are sets themselves, while others are “repeat” elements that are simply described differently. Assuming this is just a homework question, I would be happy to discuss these kinds of questions with you further—feel free to reach out!