## Discrete Mathematics MCQ Set 1

1. For some number b, (^{1}⁄_{b})^{-n} is equal to:

a) -b^{n}

b) n^{b}

c) b^{n}

d) None of the mentioned

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^{-1}reciprocal of b.

2. If ab = 1, where a and b are real numbers then:

a) a = b^{-1}

b) b = a

c) a = b = 2

d) None of the mentioned

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3. If a is a real number than a^{0} is defined as:

a) 0

b) a

c) 1

d) None of the mentioned

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4. For some number a, b and c, c^{a} x c^{b} is equal to :

a) c^{a-b}

b) c^{a+b}

c) c

d) None of the mentioned

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5. For some number a, b and c, c^{a}/c^{b} is equal to :

a) c^{a-b}

b) c^{a+b}

c) c

d) None of the mentioned

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^{b}= c

^{-b}.

6. State whether the given statement is true or false

Exponentiation is commutative.

a) True

b) False

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^{b}is not equal to b

^{A}, exponentiation is not commutative.

7. State whether the given statement is true or false

Exponentiation is associative.

a) True

b) False

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8. If 2^{a-b} = 1 then the value of a-b is equal to :

a) 1

b) 0

c) 2

d) none of the mentioned

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^{0}, so a-b = 0.

9. For some number a, b and c, a^{c} x b^{c} is equal to :

a) (ab)^{c}

b) (ac)^{b}

c) (cb)^{a}

d) None of the mentioned.

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10. If 0^{a} is not equal to zero then which of the values a cannot take :

a) 1

b) 2

c) -1

d) 0

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^{0}= 1, for any real number.

## Discrete Mathematics MCQ Set 2

1. Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then number of elements in A U B is

a) 4

b) 5

c) 6

d) 7

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2. Let the set A is {1, 2, 3} and B is { 2, 3, 4}. Then number of elements in A ∩ B is

a) 1

b) 2

c) 3

d) 4

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3. Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the set A – B is

a) {1, -4}

b) {1, 2, 3}

c) {1}

d) {2, 3}

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4. In which of the following sets A- B is equal to B – A

a) A= {1, 2, 3}, B ={2, 3, 4}

b) A= {1, 2, 3}, B ={1, 2, 3, 4}

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

d) A={1, 2, 3, 4, 5, 6}, B ={2, 3, 4, 5, 1}

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5. Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true?

a) A ≡ B U C

b) B is a singleton set.

c) A ≡ C U {2}

d) All of the mentioned

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6. If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B are respectively

a) 4, 8

b) 8, 12

c) 4, 12

d) None of the mentioned

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7. If A is {{Φ}, {Φ, {Φ}}, then the power set of A has how many element?

a) 2

b) 4

c) 6

d) 8

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8. Two sets A and B contains a and b elements respectively .If power set of A contains 16 more elements than that of B, value of ‘b’ and ‘a’ are respectively

a) 4, 5

b) 6, 7

c) 2, 3

d) None of the mentioned

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9. Let A be {1, 2, 3, 4}, U be set of all natural numbers, then U-A’(complement of A) is given by set.

a) {1, 2, 3, 4, 5, 6, ….}

b) {5, 6, 7, 8, 9, ……}

c) {1, 2, 3, 4}

d) All of the mentioned

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10. Which sets are not empty?

a) {x: x is a even prime greater than 3}

b) {x : x is a multiple of 2 and is odd}

c) {x: x is an even number and x+3 is even}

d) { x: x is a prime number less than 5 and is odd}

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## Discrete Mathematics MCQ Set 3

1. Let P (x) denote the statement “x >7.” Which of these have truth value true?

a) P (0)

b) P (4)

c) P (6)

d) P (9)

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2. Let Q(x) be the statement “x < 5.” What is the truth value of the quantification ∀xQ(x), having domains as real numbers?

a) True

b) False

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3. Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.

a) True

b) False

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4. Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?

a) True

b) False

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5. Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?

a) True

b) False

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6. The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

a) ∃x(C(x) ∧ F (x))

b) ∀x(C(x) ∧ F (x))

c) ∃x(C(x) → F (x))

d) ∀x(C(x) → F (x))

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7. The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.

a) ∀x (F (x) → P (x))

b) ∀x (F (x) ∧ P (x))

c) ∃x (F (x) ∧ P (x))

d) ∃x (F (x) → P (x))

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8. ”Everyone wants to learn cosmology.” This argument may be true for which domains?

a) All students in your cosmology class

b) All the cosmology learning students in the world

c) Both of the mentioned

d) None of the mentioned

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9. Let domain of m includes all students , P (m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English.

a) A student is there who spends more than 2 hours in playing polo

b) There is a student who does not spend more than 2 hours in playing polo

c) All students spends more than 2 hours in playing polo

d) No student spends more than 2 hours in playing polo

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10. Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers.

a) True

b) False

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## Discrete Mathematics MCQ Set 4

1. Let P and Q be statements, then P<->Q is logically equivalent to

a) P<->~Q

b) ~P<->Q

c) ~P<->~Q

d) None of the mentioned

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2. What is the negation of the statement A->(B v(or) C)?

a) A ∧ ~B ∧ ~C

b) A->B->C

c) ~A ∧ B v C

d) None of the mentioned

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3. The compound statement A-> (A->B) is false, then the truth values of A, B are respectively

a) T, T

b) F, T

c) T, F

d) F, F

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4. The statement which is logically equivalent to A∧ (and) B is

a) A->B

b) ~A ∧ ~ B

c) A ∧ ~B

d) ~(A->~B)

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5. Let P: We give a nice overall squad performance, Q: We will win the match.

Then the symbolic form of “We will win the match if and only if we give a nice overall squad performance. “is

a) P v Q

b) Q ∧ P

c) Q<->P

d) ~P v Q

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6. Let P, Q, R be true, false true , respectively, which of the following is true

a) P∧Q∧R

b) P∧~Q∧~R

c) Q->(P∧R)

d) P->(Q∧R)

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7. “Match will be played only if it is not a humid day.” The negation of this statement is

a) Match will be played but it is a humid day

b) Match will be played or it is a humid day

c) All of the mentioned statement are correct

d) None of the mentioned.

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8. Consider the following statements

A: Raju should exercise.

B: Raju is not a decent table tennis player.

C: Raju wants to play good table tennis.

The symbolic form of “Raju is not a decent table tennis player and if he wants to play good table tennis then he should exercise.” is

a) A->B->C

b) B∧(C->A)

c) C->B∧A

d) B<->A∧C

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9. The statement (~P<->Q)∧~Q is false when

a) P:True Q: False

b) P:True Q:True

c) P:False Q:True

d) P :False Q:False

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10. Let P, Q, R be true, false, false, respectively, which of the following is true

a) P∧(Q∧~R)

b) (P->Q)∧~R

c) Q<->(P∧R)

d) P<->(QvR)

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## Discrete Mathematics MCQ Set 5

1. Let A_{1}, A_{2}, be two AM’s and G_{1}, G_{2} be two GM’s between a and b,then (A_{1} + A_{2}) / G_{1}G_{2} is equal to :

a) (a+b) / 2ab

b) 2ab/(a+b)

c) (a+b)/(ab)

d) None of the mentioned

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_{1}+ A

_{2}= a + b, G

_{1}G

_{2}= ab.

2. The series a,(a+b)/2, b is in

a) AP

b) GP

c) HP

d) None of the mentioned

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3. The series a, (ab)^{1/2}, b is in

a) AP

b) GP

c) HP

d) None of the mentioned

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^{1/2}is GM between a, b. Hence series is in GP.

4. If A and G be the A.M and G.M between two positive number then the numbers are A + (A^{2} – G^{2})^{1/2}, A – (A^{2} – G^{2})^{1/2} . The given statement is

a) True

b) False

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^{2}– 2Ax + G

^{2}= 0 which implies x = A + (A

^{2}– G

^{2})

^{1/2}, A – (A

^{2}– G

^{2})

^{1/2}.

5. If one geometric mean G and two airthmetic mean A_{1}, A_{2} are inserted between two numbers,then (2A_{1} – A_{2}) (2A_{2} – A_{1}) is equal to

a) 2G

b) G

c) G^{2}

4) None of the mentioned.

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^{1/2}, A

_{1}= (2a+b)/3, A

_{2}= (a+2b)/3, (2A

_{1}– A

_{2}) = a, (2A

_{2}– A

_{1}) = b, (2A

_{1}– A

_{2})(2A

_{2}– A

_{1}) = G

^{2}.

6. State whether the given statement is true or false

AM ≤ GM.

a) True

b) False

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7. If between two numbers which are root of given equation

x^{2} – 18x + 16 = 0, a GM is inserted then the value of that GM is.

a) 4

b) 5

c) 6

d) 16

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^{2}– 2Ax + G

^{2}= 0, here G

^{2}= 16 and therefore G = 4.

8. If a_{1}, a_{2}, a_{3} are in airthemetic as well as geometric progression then which of the following is/are correct ?

a) 2a_{2} = a_{1} + a_{3}

b) a_{2} = (a_{1}a_{3})^{1/2}

c) a_{2} – a_{1} = a_{3} -a_{2}

d) All of the mentioned are correct.

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_{2}is AM, GM between a

_{1}, a

_{3}, also the series is in AP so common difference should be same.

9. If a_{1}, a_{2}, a_{3} are in GP then 1/a_{1}, 1/a_{2}, 1/a_{3} are in :

a) AP

b) GP

c) HP

d) None of the mentioned.

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10. If a_{1}, a_{2}, a_{3}…….. are in AP then if a_{7} = 15,then the value of common difference that would make a_{2} a_{7} a_{12} greatest is

a) 2

b) 0

c) 4

d) 9

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_{2}a

_{7}a

_{12}= (15 – 5d)(15)(15 + 5d) = 375(9 – d

^{2}) For maximum value d=0.