4. Let V={a, b, c, d, e, f, g} and consider the following relations:
The relation on V: R1 = {(a,a), (b,b), (c,c), (d,d), (e,e), (f,f), (g,g)}
The relation on V: R2 = {(a,a), (a,b), (b,c), (c,b), (d,e), (d,f), (f,f)}
The relation on V: R3 = {(a,a), (a,b), (b,b), (c,c), (c,d), (c,e), (d,d), (d,e), (e,e), (f,f), (g,g)}
The relation on V: R4 = {(a,a), (a,b), (b,b), (b,a), (c,c), (c,d), (c,e), (d,d), (d,c), (d,e), (e,e), (e,c), (e,d), (f,f), (g,g)}
Fill in the following table with "yes" and "no" as appropriate:
5. Shade in the region in the Venn Diagram to the right corresponding to (X∩Y')∦Z
6. List the equivalence classes for the relation on A defined by:
R = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,4), (4,5), (5,4), (5,5), (6,6), (7,7) }
7. Draw a Hasse Diagram for the relation on A defined by:
R = {(1,1), (1,2), (2,2), (3,2), (3,3), (3,4), (3,5), (4,4), (4,5), (5,5), (5,3), (5,4), (6,6), (7,5), (7,7)}
8. On extra Paper, prove one of the following using element chasing: (the 2nd may be done for extra credit)
a. X∩(Y∦Z) = (X∩Y)∦(X∩Z) b. (X∩Y)' = (X'∦Y')
9. On extra Paper, prove one of the following using Laws:
a. (A∦B) ∩ (A'∦B') = (A ∩ B') ∦ (B ∩ A') b. (A'∩B)' ∩ (A'∩C)' = A∦(B∩C)'