The document is an assignment covering topics in set theory including ordered pairs and Cartesian products. It includes various problems such as providing examples of sets, proving identities, and demonstrating that certain set operations do not commute. The assignment consists of specific tasks that require students to apply the concepts of unions, intersections, and Cartesian products.

1. DMS Sunita M Dol
Walchand Institute of Technology, Solapur Page 1
Assignment No. 8
Topics covered:
• Ordered pairs
• Cartesian product
1. Give examples of sets A, B, C such that A ∪ B = A ∪ C but B ≠ C.
2. Write the members of {a, b} × {1, 2, 3}.
3. Write A×B×C, B2
, A3
, B2
×A, and A×B where A = {1}, B = {a, b} and C =
{2, 3}.
4. Prove the identities
a. A ∩ A = A
b. A ∩ ∅ = ∅
c. A ∩ E = A
d. A ∪ E = E
5. Show by means of example A×B ≠ B×A and (A×B)×C ≠ A×(B×C).
6. Show that (A+B)+C = A+(B+C).
7. Prove that A+A =∅ and A+ ∅= A.