Lecture 3 Handout - Example Proof 2 Prove that for any two...

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Lecture 3 Handout Example Proof 1 Prove that the set of all powers of 2 (beginning with 2) is a subset of the set of all even numbers Given: Two sets A and B, } , 2 | { + = = Z j where a a A j } , 2 | { + = = Z k where k b b B Statement Justification Let x be an arbitrary element of A . We can write j x 2 = Given Rewrite as 1 2 2 - = j x Factoring Again rewrite as + = Z m where m x , 2 Substitution B x Definition of B Since x is an arbitrary element, all elements of A must be B Definition of inclusion B A Definition of subset
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Unformatted text preview: Example Proof 2 Prove that for any two sets A and B that B A B A Statement Justification Let x be an arbitrary element of B A Given B x A x and Definition of intersection Since A x , B A x Definition of union Since x is an arbitrary element, all elements of B A must be B A Definition of inclusion B A B A Definition of subset...
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This note was uploaded on 10/02/2009 for the course CSCI 1900-201 taught by Professor Billpine during the Spring '09 term at East Tennessee State University.

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