MTH645 Quiz 1 Set 2

Q1. In fuzzy sets, the value of the membership function μ(x) lies in:

1. [0, 1]
2. (–∞, ∞)
3. [–1, 0]
4. {0, 1}

Correct answer: [0, 1]

Q2. A fuzzy set can be written as:

1. A = {μA(x)}
2. A = {x, y | x ∈ μ(y)}
3. A = {x | x ∈ U}
4. A = {(x, μA(x)) | x ∈ U}

Correct answer: A = {(x, μA(x)) | x ∈ U}

Q3. In classical (crisp) sets, the membership function can take which values?

1. Between –1 and 1
2. Between 0 and 10
3. Any real number
4. Only 0 or 1

Correct answer: Only 0 or 1

Q4. How many elements are there in the power set of a set containing 3 elements?

1. 8
2. 6
3. 9
4. 3

Correct answer: 8

Q5. Which of the following is the correct definition of a set?

1. A group of numbers only
2. A group of identical objects only
3. A collection of well-defined and distinct objects
4. A list of random numbers

Correct answer: A collection of well-defined and distinct objects

Q6. What does μA(x) = 0 mean?

1. x does not belong to set A
2. None of these
3. x partially belongs to set A
4. x fully belongs to set A

Correct answer: x does not belong to set A

Q7. A membership function represents:

1. The degree of belongingness of an element to a set
2. The power of a fuzzy set
3. The intersection of two sets
4. The total number of elements in a set

Correct answer: The degree of belongingness of an element to a set

Q8. The number of elements in the power set of a set with n elements is given by:

1. n!
2. n
3. 2ⁿ
4. n²

Correct answer: 2ⁿ

Q9. Which of the following is not a valid membership value?

1. 1.5
2. 1
3. 0.4
4. 0

Correct answer: 1.5

Q10. The union of two fuzzy sets A and B is defined as:

1. μA∈B(x) = max(μA(x), μB(x))
2. μA∈B(x) = μA(x) * μB(x)
3. μA∈B(x) = min(μA(x), μB(x))
4. μA∈B(x) = μA(x) + μB(x)

Correct answer: μA∈B(x) = max(μA(x), μB(x))