Question

Explain if you have A−B and B−A, are equivalent? Always, Sometimes, or neven? Write our your explanation and also show Venn Diagram

Answer 1

The sets A−B and B−A are not always equivalent. If A and B have some elements in common, then A−B and B−A will not be the same, as there will be elements in the sets that are not present in the other set. However, if A and B have no elements in common, then A−B and B−A will be the same.

Step-by-step explanation:

The sets A−B and B−A are not always equivalent. The set A−B represents the elements that are in set A but not in set B, while the set B−A represents the elements that are in set B but not in set A.

If A and B have some elements in common, then A−B and B−A will not be the same, as there will be elements in the sets that are not present in the other set.

For example, if A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A−B = {1, 2} and B−A = {5, 6}. These sets are not equivalent. However, if A and B have no elements in common, then A−B and B−A will be the same, as there are no elements to exclude from the sets.

Regarding the Venn diagram, we can represent the sets A and B as overlapping circles, where the common region represents the elements that are in both sets. The region specific to A represents the elements unique to set A, and the region specific to B represents the elements unique to set B.