Relations, Diagrams and Sets

Question

1) If R is a reflexive relation on set A, prove that R² is also reflexive.

2) Draw a Hasse Diagram for subsets P(U), where U={1,2,3,4}

3) Determine whether each of the following collections of sets is a partition for the given set A. If the collection is not a partition, explain why it fails to be.
A= {1,2,3,4,5,6,7,8}
A1= {4,5,6}
A2= {1,8}
A3= {2,3,7}

4) Let A = {1,2,3,4,5,6,7,8}. In how many ways can we partition A as A1 U A2 U A3 with:
1,2 is an element of symbol A
3,4 is an element of symbol A2
5,6,7 is an element of symbol A3

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