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Unformatted text preview: NUMBERS AND SETS EXAMPLES SHEET 1. W. T. G. 1. Let A , B and C be three sets. Give a proof that A \ ( B C ) = ( A \ B ) ( A \ C ) using the criterion for equality of sets. 2. The symmetric difference A 4 B of A and B is defined to be ( A \ B ) ( B \ A ). (That is, it is the set of elements that belong to one of A and B but not both.) Write out a truth table to show that the operation 4 is associative. Show that x belongs to A 4 ( B 4 C ) if and only if x belongs to an odd number of the sets A , B and C and use this observation to give a second proof that 4 is associative. 3. Let A , B , C and D be sets. Prove that A ( B C ) = ( A B ) ( A C ). Is it necessarily true that ( A B ) ( C D ) = ( A C ) ( B D )? 4. Write down the negations of the following statements. (i) n is even or m is a multiple of 3. (ii) Every x A is also an element of B C ....
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This note was uploaded on 03/06/2012 for the course MATH 508 taught by Professor Staff during the Fall '10 term at UPenn.
- Fall '10