# Need some help with a set question:

• November 8th 2012, 06:53 PM
Linseykathleen
Need some help with a set question:
If (A is a subset B) and (C is a subset of D), then (A intersection C) is a subset of (B intersection D).

I think I have a correct answer, but I'm uncertain (I feel like I'm leaving something out and that there should be something between the last two lines that explains further) so if you can answer/explain, that would be super helpful. Thanks in advance!

Here's what I have:

Let x be an element of A intersect C.
Since we know A is a subset of B, then we know that x is an element of A and therefore is an element of B too.
Also, since C is a subset of D and x is an element of C then x is also an element of D too.
This shows that A intersect C is a subset of B intersect D.

• November 8th 2012, 11:00 PM
chiro
Re: Need some help with a set question:
Hey Linseykathleen.

I don't know about how your professor/lecturer/whatever expects of proofs but if you need a really rigorous one try considering that if A is a subset of B then A intersection B = A for all A and B such that A is a subset of B.

This way if (A and C) is a subset of (B and D), then (A and C) and (B and D) = (A and C).
• November 8th 2012, 11:46 PM
jakncoke
Re: Need some help with a set question:
Quote:

Originally Posted by chiro
Hey Linseykathleen.

I don't know about how your professor/lecturer/whatever expects of proofs but if you need a really rigorous one try considering that if A is a subset of B then A intersection B = A for all A and B such that A is a subset of B.

This way if (A and C) is a subset of (B and D), then (A and C) and (B and D) = (A and C).

i thought her argument was rigorous enough. From my experience to show $A \subset B$. You assume $x \in A$ and show $x \in B$. So, she assumed $x \in A \cap C$ and showed $x \in B \cap D$