Help in understanding a set theory proof

[muted jacinth]

I don't understand why the text supposed that C = A (what if C ≠ A)? Drawing a Venn diagram of the situation does not seem to help either; in fact it seems to disprove the background direction of the theorem.

[slate granite]

You're just considering a specific case that leads you to your solution. You're trying to find a specific subset, not work with every possible subset

[muted jacinth]

Why should I care about only a specific case?

[slate granite]

Because that specific case is sufficient to prove that A is a subset of B

[mortal sorrel]

try with simple examples

[muted jacinth]

I'm still confused

[slate granite]

You want to show that A is a subset of B. You are given that every subset of A is also a subset of B. But A is a subset of A, so from what you were given, you can conclude that it must also be a subset of B.

[muted jacinth]

That makes more sense to me

I realized I just misunderstood the statement

[muted jacinth]

Thank u very much for clarifying it to me

.close