Given U = {1, 2, 3, 4, 5, 6, 7} A = {(3, 0.7), (5, 1), (6, 0.8)} then…

Key idea: In a fuzzy set, the complement's membership value for each element is 1 minus the element's membership in the original fuzzy set.

• Universe U = {1, 2, 3, 4, 5, 6, 7}.

• Given fuzzy set A has memberships: 3 → 0.7, 5 → 1, 6 → 0.8. All other elements in U have membership 0 in A.

• Compute complement memberships using 1 - μA(x):

• For 1: μA(1) = 0 → μ~A(1) = 1 - 0 = 1

• For 2: μA(2) = 0 → μ~A(2) = 1 - 0 = 1

• For 3: μA(3) = 0.7 → μ~A(3) = 1 - 0.7 = 0.3

• For 4: μA(4) = 0 → μ~A(4) = 1 - 0 = 1

• For 5: μA(5) = 1 → μ~A(5) = 1 - 1 = 0

• For 6: μA(6) = 0.8 → μ~A(6) = 1 - 0.8 = 0.2

• For 7: μA(7) = 0 → μ~A(7) = 1 - 0 = 1

Therefore the full explicit complement is: {(1, 1), (2, 1), (3, 0.3), (4, 1), (5, 0), (6, 0.2), (7, 1)}

Note: Some answers omit elements with zero membership (for example omitting (5, 0)). That omission is acceptable only if the context permits leaving out zero-membership elements; otherwise include all elements of the universe as shown above.

The provided choice that lists {(1, 1), (2, 1), (3, 0.3), (4, 1), (6, 0.2), (7, 1)} matches the complement values but omits (5, 0). For a complete explicit answer include (5, 0) as shown.