Answer to Question #299327 in Abstract Algebra for Jlove

Question

1. Prove: A∪B∪C=A∪(B∪C)

2. Prove: A∩B'=A'∪B'

3. Given nU=692, nA=300, nB=230, nC=370, nA∩B=150, nA∩C=180, nB∩C=90, nA∩B'∩C'=10 where n(S) is the number of distinct elements in the set S, find:

a. n(A∩B∩C) c. n(A'∩B'∩C')

b. n(A'∩B∩C') d. n((A∩B)∪(A∩C)∪(B∩C)

4. Show that total number of proper subsets of S={a1,a2,… an} is 2n=1.

5. Show that multiplication is a binary operation on S={1,-1, i, -i} where i=-1.

6. Show that “is a factor of” on N is reflexive and transitive but is not symmetric.