Note: ^ = "intersects"; U = "union"

Prove that A ^ B ^ C "is a subset of" D, where D = (B ^ (A U C)) U (C ^ A)

Obviously, when drawing a Venn diagram, they all will meet at the very middle. How can I prove this is true, in a formal proof.

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- May 9th 2006, 07:01 PMPhilipJProving a Set
Note: ^ = "intersects"; U = "union"

Prove that A ^ B ^ C "is a subset of" D, where D = (B ^ (A U C)) U (C ^ A)

Obviously, when drawing a Venn diagram, they all will meet at the very middle. How can I prove this is true, in a formal proof. - May 9th 2006, 07:15 PMThePerfectHackerQuote:

Originally Posted by**PhilipJ**

If there is nothing to prove because the empty set is subset of every set.

If not then, such as

Notice that because and .

Thus,

Thus, any element of is element of . Thus, by definition,

- May 9th 2006, 07:24 PMThePerfectHacker
Also, using the "transitive" property of subsets:

and then,

And the property,

And finally the property,

---------------

Thus,

Because

And,

Because

Thus, (by transitive propetry),