Which of the following is an example of two sets A and B such that A ∪ B = A
(a) A = {1, 2, 6, 7} B = {2, 6, 7}        (b) A = {-1, 0, 6, 9} B = {-2, 6, 8}

Solution:

For the given sets A and B:

(a) A = {1, 2, 6, 7} and B = {2, 6, 7}. Hence,  A ∪ B = {1, 2, 6, 7} ∪ {2, 6, 7} = {1, 2, 6, 7} = A

(b) A = {-1, 0, 6, 9} and B = {-2, 6, 8}. Hence, A ∪ B = {-1, 0, 6, 9} ∪ {-2, 6, 8} = {-1, 0, -2, 6, 8, 9} ≠ A

Thus, the sets A and B in part (a) satisfies A ∪ B = A

Which of the following is an example of two sets A and B such that A ∪ B = A

Summary:

Option(a) A = {1, 2, 6, 7}, B = {2, 6, 7} is an example of two sets A and B such that A ∪ B = A.