Question

hi guys can someone help me whit this question is for tommorow for my is so difficult . The exercise talks about math sets. It is: give three examples of sets A and B such that AU(union)B=B​

Answer 1

(i) A = {1}, B = {1, 2}, (ii) A = empty set, B = {1, 2, 3}, (iii) A = {a, b, c}, B = {a, b, c}, (iv) A = {7, 8, 9, 10}, B = {7, 8, 9, 10, 11, 12}

Explanation:

The idea: A U B = the set of all elements (from a Universal set, like the set of all integers) that are in at least one of the sets A or B. So, for the equation A U B = B to be true, the set A must be a subset of the set B, because otherwise A U B would contain at least one element not in B, making the equation A U B = B false (set B would be a proper subset of A U B). So, if A = {1, 2, 3, 4} and B = {1, 2, 3}, then A U B = {1, 2, 3, 4}, and A U B = B would be false. However, if A = {1, 2, 3} and B = {1, 2, 3, 4}, then A U B = B would be true.