Question

Suppose that A, B, and C are sets such that A is a subset of B and B is a subset of C. Show that A is a subset of C.

Answer 1

Is this how I would show it for a homework assignment or test? I figured there would be some sort of formal proof I had no idea how to do

Answer 2

Transitive property?

Answer 3

What you can do, is say since \(A \subseteq B \), when we know that for every \(x \in A\), then \(x \in B\)

Answer 4

And since all \(x \in B\) are in \(C\), that is \(x \in C\) because \(B \subseteq C\), then it follows that for all \(x \in A\), we have \(x \in C\), so \(A \subseteq C\).

Answer 5

Thank you very much!

Answer 6

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