h6 - is an equivalence relation. Question 4. Let R be the...

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HOMEWORK 6 Question 1. Prove that if A , B and C are any sets, then A × ( B C ) = ( A × B ) ( A × C ) . Question 2. (a) Prove that if A , B , C and D are any sets, then ( A × B ) ( C × D ) ( A C ) × ( B D ) . (b) Give an example of sets A , B , C and D such that ( A × B ) ( C × D ) 6 = ( A C ) × ( B D ) . Question 3. Let S = { ( a,b ) | a,b Z ,b 6 = 0 } and let be the relation defined on S by ( a,b ) ( c,d ) iff ad = bc. Prove that
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Unformatted text preview: is an equivalence relation. Question 4. Let R be the relation on R r { } dened by a R b iff a b Q or a-b Q . Determine whether R is an equivalence relation. ( Hint: You may make use of the fact that 2 / Q .) 1...
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This note was uploaded on 01/31/2011 for the course MATH 300 taught by Professor Ctw during the Spring '08 term at Rutgers.

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