Solution

The correct answer is {(x1, 0.3), (x2, 0.2), (x3, 0.4)}

Key Points

To find the intersection (denoted by ∩) of two fuzzy sets, we take the minimum membership value for each corresponding element in the sets. Given the fuzzy sets:

• A = {(x1, 0.3), (x2, 0.7), (x3, 0.4)}
• B = {(x1, 0.5), (x2, 0.2), (x3, 0.5)}

The intersection ( A ∩ B ) is:

• For ( x1 ), the minimum membership value is min(0.3, 0.5) = 0.3.
• For ( x2 ), the minimum membership value is min(0.7, 0.2) = 0.2.
• For ( x3 ), the minimum membership value is min(0.4, 0.5) = 0.4.

Thus, the fuzzy set ( A ∩ B ) is: ( {(x1, 0.3), (x2, 0.2), (x3, 0.4)} )

The correct answer is: 4) {(x1, 0.3), (x2, 0.2), (x3, 0.4)}