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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Originally Posted by PhilipJ 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. 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,
Also, using the "transitive" property of subsets: and then, And the property, And finally the property, --------------- Thus, Because And, Because Thus, (by transitive propetry),
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