## Discrete Mathematics MCQ Set 1

1. For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {a_{n}} is ____________

a) 3^{n+1} – 2

b) 3^{n} – 2

c) (-3)^{n} + 4

d) n^{2} – 2

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^{n}} which is 3, 9, 27 …. Comparing these terms with the corresponding terms of sequence {3

^{n}} and the nth term is 2 less than the corresponding power of 3.

2. For the sequence 0, 1, 2, 3 an is ____________

a) ⌈n/2⌉+⌊n/2⌋

b) ⌈n/2⌉+⌈n/2⌉

c) ⌊n/2⌋+⌊n/2⌋

d) ⌊n/2⌋

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3. The value of∑(k=50)^{100} k^{2} is __________

a) 338,350

b) 297,900

c) 297,925

d) 290,025

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^{n}k

^{2}= (n(n + 1)(2n + 1)) / 6.

4. The sets A and B have same cardinality if and only if there is ___________ from A to B.

a) One-to-one

b) One-to-many

c) Many-to-many

d) Many-to-one

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5. For the sequence a_{n} = ⌊√2n+ 1/2⌋, a_{7}is ____________

a) 1

b) 7

c) 5

d) 4

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_{7}= ⌊√14+1/2⌋ which is ⌊4.24⌋ = 4.

6. The value of ∑(i=1)^{3} ∑(h=0)^{2} i is _________

a) 10

b) 17

c) 15

d) 18

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^{3}∑(h=0)

^{2}i = 1+1+1+2+2+2+3+3+3 = 18.

7. For the sequence a_{n} = 6. (1/3)^{n}, a_{4} is _________

a) 2/25

b) 2/27

c) 2/19

d) 2/13

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8. The value of ∑(i=0)^{4}i! is __________

a) 32

b) 30

c) 34

d) 35

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9. Set of all integers is counter. Is it True or False?

a) True

b) False

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10. The value of ∏( k=1)^{100} (-1) ^{k} is _________

a) 0

b) 1

c) -1

d) 2

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_{1}, a

_{2}, a

_{3}…… a

_{n}is represented by ∏(i=1)

^{n}a

_{i}.

## Discrete Mathematics MCQ Set 2

1. The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________

a) {1, 2, 6, 1}

b) {1, 2, 5, 6}

c) {1, 2, 1, 2}

d) {1, 5, 6, 3}

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2. The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________

a) {1, 2}

b) {5, 6}

c) {2, 5}

d) {1, 6}

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3. Two sets are called disjoint if there _____________ is the empty set.

a) Union

b) Difference

c) Intersection

d) Complement

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4. Which of the following two sets are disjoint?

a) {1, 3, 5} and {1, 3, 6}

b) {1, 2, 3} and {1, 2, 3}

c) {1, 3, 5} and {2, 3, 4}

d) {1, 3, 5} and {2, 4, 6}

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5. The difference of {1, 2, 3} and {1, 2, 5} is the set ____________

a) {1}

b) {5}

c) {3}

d) {2}

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6. The complement of the set A is _____________

a) A – B

b) U – A

c) A – U

d) B – A

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7. The bit string for the set {2, 4, 6, 8, 10} (with universal set of natural numbers less than or equal to 10) is ____________________

a) 0101010101

b) 1010101010

c) 1010010101

d) 0010010101

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8. Let Ai = {i, i+1, i+2, …..}. Then set {n, n+1, n+2, n+3, …..} is the _________ of the set Ai.

a) Union

b) Intersection

c) Set Difference

d) Disjoint

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9. The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________

a) 1010100000

b) 1010101101

c) 1111111100

d) 1111101010

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10. The set difference of the set A with null set is __________

a) A

b) null

c) U

d) B

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## Discrete Mathematics MCQ Set 3

1. A __________ is an ordered collection of objects.

a) Relation

b) Function

c) Set

d) Proposition

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2. The set O of odd positive integers less than 10 can be expressed by _____________

a) {1, 2, 3}

b) {1, 3, 5, 7, 9}

c) {1, 2, 5, 9}

d) {1, 5, 7, 9, 11}

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3. Power set of empty set has exactly _________ subset.

a) One

b) Two

c) Zero

d) Three

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4. What is the Cartesian product of A = {1, 2} and B = {a, b}?

a) {(1, a), (1, b), (2, a), (b, b)}

b) {(1, 1), (2, 2), (a, a), (b, b)}

c) {(1, a), (2, a), (1, b), (2, b)}

d) {(1, 1), (a, a), (2, a), (1, b)}

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5. The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or False?

a) True

b) False

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6. What is the cardinality of the set of odd positive integers less than 10?

a) 10

b) 5

c) 3

d) 20

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7. Which of the following two sets are equal?

a) A = {1, 2} and B = {1}

b) A = {1, 2} and B = {1, 2, 3}

c) A = {1, 2, 3} and B = {2, 1, 3}

d) A = {1, 2, 4} and B = {1, 2, 3}

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8. The set of positive integers is _____________

a) Infinite

b) Finite

c) Subset

d) Empty

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9. What is the Cardinality of the Power set of the set {0, 1, 2}.

a) 8

b) 6

c) 7

d) 9

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10. The members of the set S = {x | x is the square of an integer and x < 100} is ________________

a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}

b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}

d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

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## Discrete Mathematics MCQ Set 4

1. A polygon with 7 sides can be triangulated into

a) 7

b) 14

c) 5

d) 10

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2. Every simple polynomial has an interior diagonal.

a) True

b) False

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3. A polygon with 12 sides can be triangulated into

a) 7

b) 10

c) 5

d) 12

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4. Let P(n) be the statement that a postage of n cents can be formed using just 3-cents stamps and 5-cents stamps. Is the statements P(8) and P(10) are Correct?

a) True

b) False

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5. Which amount of postage can be formed using just 4-cent and 11-cent stamps?

a) 2

b) 5

c) 30

d) 10

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6. 22-cent of postage can be produced with two 4-cent stamp and one 11-cent stamp.

a) True

b) False

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7. Which amount of postage can be formed using just 3-cent stamp and 10-cent stamps?

a) 27

b) 20

c) 11

d) 5

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8. Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true.

a) P(3)

b) P(2)

c) P(4)

d) P(6)

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9. Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.

a) P(1)

b) P(2)

c) P(4)

d) P(n)

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10. A polygon with 25 sides can be triangulated into

a) 23

b) 20

c) 22

d) 21

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## Discrete Mathematics MCQ Set 5

1. Let the statement be “If n is not an odd integer then square of n is not odd.”,then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For a direct proof we should proove

a) ∀nP ((n) → Q(n))

b) ∃ nP ((n) → Q(n))

c) ∀n~(P ((n)) → Q(n))

d) ∀nP ((n) → ~(Q(n)))

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2. Which of the following can only be used in disproving the statements?

a) Direct proof

b) Contrapositive proofs

c) Counter Example

d) Mathematical Induction

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3. Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”,then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be

a) ∀nP ((n) → Q(n))

b) ∃ nP ((n) → Q(n))

c) ∀n~(P ((n)) → Q(n))

d) ∀n(~Q ((n)) → ~(P(n)))

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4. When to proof P→Q true, we proof P false, that type of proof is known as

a) Direct proof

b) Contrapositive proofs

c) Vacuous proof

d) Mathematical Induction

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5. In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

a) Direct proof

b) Proof by Contradiction

c) Vacuous proof

d) Mathematical Induction

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6. A proof covering all the possible cases, such type of proofs are known as

a) Direct proof

b) Proof by Contradiction

c) Vacuous proof

d) Exhaustive proof

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7. Which of the arguments is not valid in proving sum of two odd number is not odd.

a) 3 + 3 = 6 ,hence true for all

b) 2n +1 + 2m +1 = 2(n+m+1) hence true for all

c) All of the mentioned

d) None of the mentioned

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8. A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as

a) Direct proof

b) Contrapositive proofs

c) Vacuous proof

d) Proof by cases

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9. A proof that p → q is true based on the fact that q is true, such proofs are known as

a) Direct proof

b) Contrapositive proofs

c) Trivial proof

d) Proof by cases

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10. A theorem used to prove other theorems is known as

a) Lemma

b) Corollary

c) Conjecture

d) None of the mentioned