Discrete Math Problem: Proving Subset Relationships in Sets A, B, and C

[sportlover36]

One of my homework problems says is this true or false and prove your answer:

For all sets A, B, C if A n C is a subset of B n C then A is a subset of B.

I believe the answer is true but i have no idea please help!

 

[vela]

What are the definitions of subset and intersection?

 

[sportlover36]

If A is a subset of B that means that if there is an element x in A then x is also an elemnt of B. And A n B means x is an element of A and B

 

[vela]

Good! So assume $x\in A$. You want to show that $x \in B$. All you know is that $A \cap C \in B \cap C$.

If you run into problems proving it, you may realize the problem is there because it's a counterexample of what you're trying to prove.

 

[daveyinaz]

Consider
$$A = \{ 1, 3 \}$$
$$B = \{ 1, 2, 4 \}$$
$$C = \{ 1, 2 \}$$