Set Operations with Universal Set U = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} - Find A∩B, B̅ \ A, and (A∪B-𝐴∩𝐵) ∩ (B ∪ 𝐴̅)

(i) The elements in set A are: {-3, -2, -1, 0, 1, 2, 3}.

To find A∩B, we need to find the elements that are common to both sets A and B. The common elements are {-3, -1, 1, 3}. Therefore, A∩B = {-3, -1, 1, 3}.

To find B̅ \ A, we need to find the elements in the complement of set B (B̅) that are not in set A. The complement of set B is all the elements in the universal set U that are not in set B. Therefore, B̅ = {-5, -4, -2, 0, 2, 4, 6}. The elements that are in B̅ but not in A are {-5, -4, -2, 0, 2, 4, 6}. Therefore, B̅ \ A = {-5, -4, -2, 0, 2, 4, 6}.

(ii) To find (A∪B-𝐴∩𝐵) ∩ (B ∪ 𝐴̅), we first need to find A∪B, which is the union of sets A and B. The union of sets A and B is {-5, -4, -3, -2, -1, 0, 1, 2, 3, 5, 7}.

Next, we need to find A∩B, which we already found to be {-3, -1, 1, 3}.

Now, we can find (A∪B-𝐴∩𝐵) ∩ (B ∪ 𝐴̅) by taking the elements that are common to both sets (A∪B-𝐴∩𝐵) and (B ∪ 𝐴̅). The common elements are {-5, -4, -2, 0, 2, 4}. Therefore, (A∪B-𝐴∩𝐵) ∩ (B ∪ 𝐴̅) = {-5, -4, -2, 0, 2, 4}.