Discrete Mathematics Week 2 NPTEL

Course name: Discrete Mathematics

1) If A and B are sets and A ∪ B = A ∩ B, then which of the following is(are) true?

1. Either one of A or B is an empty set.
2. B is a proper subset of A.
3. A = B
4. A is a proper subset of B.

ANSWER: 3.A = B

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2) If A = {3,3,4,5,6,6,9}, B = {{5,9},12,{1,{x,y}},{a,b,c}}, C = {ϕ}, X = {x,y,z} and Y = {A,B}. Which statement is true?

1. Cardinality of A is 7
2. Cardinality of B is 4
3. Cardinality of C is 0
4. Cardinality of X is 2
5. Cardinality of Y is 3

ANSWER: 2.Cardinality of B is 4

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3) Let A = {3,5,6,7,8,9}, B={2,4,5,11,14} and C = {-1,0,1}. Which of the following is not a disjoint set?

1. A and C
2. B and C
3. C and A ∪ B
4. A and B

ANSWER: 4.A and B

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These are answers for Discrete Mathematics Week 2

4) Let set A = {4,5,6,7,9} and P(A) denote the power set of A. What is the cardinality of P(P(A))?

1. 2^16
2. 2^32
3. 2^10
4. 2^5

ANSWER: 2.2^32

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5) Let A ={x | x ∈ Z; -2 ≤ x ≤ 5} and B ={ x | x ∈ N; x is a prime number}, what is A−B?

1. {-2,-1,0,1}
2. {1,4}
3. {-2,-1,0,1,4}
4. {-2,-1,0,1,2,3,4,5}

ANSWER: 3.{-2,-1,0,1,4}

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Discrete Mathematics Week 2 NPTEL Assignment Solution

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6) In a group of 120 people, 50 people love to eat dairy milk chocolate, 70 people love to eat Kitkat, and 20 people do not like any type of chocolate. How many people love to eat both types of chocolate?

1. 20
2. 30
3. 10
4. 40

ANSWER: 1.20

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7) Which of the following pairs of sets are equal?

1. X={x | x ∈ Z; 0 ≤ x ≤ 6} and Y={x | x ∈ R; x < 7}
2. X, the set of letters in “THYMIER” and Y, the set of letters in “THYMINE”
3. A = {-2,-3}, B = {x:x is a Solution of x2+5x+6=0}
4. A = {0}; B = {x: x is a positive integral root of the equation x2−x−42=0

ANSWER: 3.A = {-2,-3}, B = {x:x is a Solution of x2+5x+6=0}

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8) Suppose A = {1,2,3,4}. How many subsets of 2 distinct elements are possible?

1. 4
2. 6
3. 5
4. 7

ANSWER: 2.(6)

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9) Simplify (A’∩B’)’∪B

1. A’∪B’
2. B’
3. A’∩B
4. A’∪B

ANSWER: 4.A’∪B

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10) The set O of odd positive integers less than or equal to 10 is _________.

1. {1,2,3}
2. {1,3,5,7,9}
3. {1,2,5,7,9}
4. {0,1,3,5,7,9}

ANSWER: 2.{1,3,5,7,9}

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