Problem 6E
Prove the identity laws in Table 1 by showing that
a) A ∪ ∅ = A.
b) A ∩ U = A.
Solution:
Step 1:
NOTE: A set A is a subset of a set B , or equivalently B is a superset of A , if A is contained inside B, that is all elements of A are also elements of B. A and B may coincide.That is

UNION: The union of two sets A and B is the set containing all elements that are in A or in B ( possibly both).
Then it is denoted by , we can write if and only if or .
Note :
Example :
A= { a, b} , B = {b ,c} then .
The union of sets A and B is shown by the shaded area in the venn diagram: