# Thread: Cartesian product over union

1. ## Cartesian product over union

Prove that for any sets A, B, C, D;

(AxB)U(CxD) is a subset of (AUC) x (BUD).

Give an example to show that the reverse inclusion need not hold.

2. Write in symbolic form what the following means.

1. A subset (every element of one set is an element of the other).

2. An element of (AxB)U(CxD)

3. An element of (AUC) x (BUD).

The result should be a proposition consisting of logical connectives and things like $x\in A$ or $y\in D$. Is this proposition true?

You will not be able to solve this problem until you know the definitions of a subset, a Cartesian product and a union and are able apply those definitions to this situation.

I have managed to prove this now.

4. It is not a good habit to ask for help before doing your job or offort.

5. Originally Posted by emakarov
Write in symbolic form what the following means.

1. A subset (every element of one set is an element of the other).

2. An element of (AxB)U(CxD)

3. An element of (AUC) x (BUD).

The result should be a proposition consisting of logical connectives and things like $x\in A$ or $y\in D$. Is this proposition true?

You will not be able to solve this problem until you know the definitions of a subset, a Cartesian product and a union and are able apply those definitions to this situation.
There are not only Venn diagram method .I think it is vital to proof this example by using proof by definition method.

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### prove that (AÃ—B)U(CÃ—D)=(AUC)Ã—(BUD)

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