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## Discrete Mathematics MCQ Set 1

1. If a set contains 3 elements then the number of subsets is
a) 6
b) 3
c) 12
d) 8

Answer: d [Reason:] For elements with n elements the number of subsets are 2n.

2. The set containing all the collection of subsets is known as
a) Subset
b) Power set
c) Union set
d) None of the mentioned

Answer: b [Reason:] Power set contains all the subsets as its elements.

3. If a set is empty then number of subsets will be
a) 1
b) 2
c) 0
d) 4

Answer: a [Reason:] The set has zero elements so 2o = 1.

4. If the number of subsets of a set are 4 then the number of elements in that sets are
a) 1
b) 2
c) 3
4) 4

Answer: b [Reason:] The number of elements be x then x2 = 4 thus x=2.

5. State whether the given statement is true or false
The number of subsets of a set is 5.
a) True
b) False

Answer: b [Reason:] The number of subsets will always be a power of 2.

6. State whether the given statement is true or false
The number of subsets of a set can be odd or even.
a) True
b) False

Answer: a [Reason:] The number of subsets will be odd in case of empty set otherwise even.

7. Let a set be A={1, 2, 3} then the number of subsets containing two elements will be
a) 4
b) 3
c) 5
d) 8

Answer: b [Reason:] The subsets will be {1, 2}, {2, 3}, {1, 3}.

8. Let the set be A= {a , b, c, {a,b}} then which of the following is false
a) {a, b} Є A
b) a Є A
c) {a} Є A
d) b, c ЄA

Answer: c [Reason:] Only elements belongs to a set, {a} is a subset of this set.

9. If A={1, 2, 3, 4} ,then the number of the subsets of A that contain the element 2 but not 3, is:
a) 16
b) 4
c) 8
d) 24

Answer: b [Reason:] The subsets would be {1, 2, 4},{1, 2}, {2, 3}, {2}.

10. Let A(1), A(2), A(3),……..,A(100) be 100 sets such that number of elements in A(i)=i+1 and A(1) is subset of A(2), A(2)is subset of A(3),…..,A(99) is subset of A(100). The the number of elements in union of the all the sets are: n(A(1) U A(2) U A(3) …..U A(100)):
a) 99
b) 100
c) 101
d) 102

Answer: c [Reason:] Since all sets are subsets of A(100) therfore in union only elements of A(100)will come.A(100) contains 101 elements.

## Discrete Mathematics MCQ Set 2

1. Let C and D be two sets then which of the following statements are true?
1) C U D = D U C
2) C ∩ D = D ∩ C
a) Both of the statements
b) Only 1st statement
c) Only 2nd statement
d) None of the statements

Answer: a [Reason:] Commutative laws hold good in sets.

2. If set C is {1, 2, 3, 4} and C – D = Φ then set D can be
a) {1, 2, 4, 5}
b) {1, 2, 3}
c) {1, 2, 3, 4, 5}
d) None of the mentioned

Answer: c [Reason:] C ∩ D should be equivalent to C for C – D = Φ.

3. Let C and D be two sets then C – D is equivalent to
a) C’ ∩ D
b) C‘∩ D’
c) C ∩ D’
d) None of the mentioned

Answer: c [Reason:] Set C-D will be having those elements which are in C but not in D.

4. For two sets C and D the set (C – D) ∩ D will be
a) C
b) D
c) Φ
d) None of the mentioned

Answer: c [Reason:] C-D ≡ C ∩ D’, D ∩ D’ ≡ Φ.

5. Which of the following statement regarding sets is false
a) A ∩ A = A
b) A U A = A
c) A – (B ∩ C) = (A – B) U (A –C)
d) (A U B)’ =A’ U B’

Answer: d [Reason:] (A U B)’ = A’ ∩ B’.

6. Let C = {1,2,3,4} and D = {1, 2, 3, 4} then which of the following hold not true in this case
a) C – D = D – C
b) C U D = C ∩ D
c) C ∩ D = C – D
d) C – D = Φ

Answer: c [Reason:] C ∩ D = {1, 2, 3, 4} ≠ Φ.

7. If C’ U (D ∩ E’) is equivalent to
a) (C ∩ (D U E))’
b) (C ∩( D∩ E’))’
c) (C ∩( D’ U E))’
d) (C U ( D ∩ E’)’

Answer: c [Reason:] (C’)’≡ C, (C∩ D)’ ≡ C’ U D’.

8. Let Universal set U is {1, 2, 3, 4, 5, 6, 7, 8} ,(Complement of A) A’ is {2, 5, 6, 7}, A ∩ B is {1, 3, 4} then the set B’ will surely have of which of the element
a) 8
b) 7
c) 1
d) 3

Answer: a [Reason:] The set A is {1,3,4,8} and thus surely B does not have 8 in it. Since 8 does not belong to A ∩ B. For other element like 7 we can’t be sure.

9. Let a set be A then A ∩ φ and A U φ are respectively
a) φ, φ
b) φ, A
c) A, φ
d)None of the mentioned

Answer: b [Reason:] By Domination Laws on sets.

10. If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set A U B U C will be
a) 8
b) 14
c) 22
d) 15

Answer: a [Reason:] For minimum elements set B and C have 8 elements each and all of the elements are same, Also set A should have 7 elements which are already present in B and C. Thus A U B U C ≡ A ≡ B.

## Discrete Mathematics MCQ Set 3

1. An Algorithm is:
a) A procedure for solving a problem
b) A problem
c) A real life mathematical problem
d) None of the mentioned

Answer: a [Reason:] An algorithm is stepwise solution to the problem.

2. An algorithm in which we divide the problem into subproblem and then we combine the subsolutions to form solution to the original problem is known as:
a) Brute Force
b) Divide and Conquer
c) GreedyAlgorithm
d) None of the mentioned

Answer: b [Reason:] In Divide and Conquer we divide the problem and then recombine the solution.

3. An algorithm which uses the past results and and uses them to find the new results is
a) Brute Force
b) Divide and Conquer
c) Dynamic programming algorithms
d) None of the mentioned

Answer: c [Reason:] In Dynamic programming algorithms we utilizes previous results for new ones.

4. A Complexity of algorithm depends upon:
a) Time only
b) Space only
c) Both Time and Space
4) None of the mentioned

Answer: c [Reason:] For Complexity we calculate both time and space consumed.

5. An algorithm which tries all the possibilities unless results are satisfactory is and genrally is time consuming is:
a) Brute Force
b) Divide and Conquer
c) Dynamic programming algorithms
d) None of the mentioned

Answer: a [Reason:] In Brute force all the possibilties are tried.

6. For a recursive algorithm :
a) a base case is necessary and is solved without recursion.
b) a base case is not necessary
c) doesnot solve a base case directly
d) none of the mentioned

Answer: b [Reason:] Base case ends recursion and therefore it is necessary for finite recurssion.

7. Optimization of algorithm means:
a) making that algorithm fast by time and compact by space
b) making that algorithm slow by time and large by space
c) making that algorithm fast by time and large by space
d) making that algorithm slow by time and compact by space

Answer: a [Reason:] An Algorithm should be fast and compact.

8. For an algorithm which is most important charecterstic that makes it acceptable:
a) Fast
b) Compact
c) Correctness and Precision
d) None of the mentioned

Answer: c [Reason:] An algorithm should be correct otherwise it’s of no use even if it is fast and compact.

9. An algorithm: can be represented through:
a) flow charts
b) pseudo codes
c) instructions in common language
d) all of the mentioned

Answer: d [Reason:] Algorithm is represented through pseudo codes, normal language sentences or flow charts.

10. There are two algorithms suppose A takes 1.41 milli seconds while B take 0.9 milliseconds,Which one of them is better considering all other things same.
a) A is better than B
b) B is better than A
c) Both are equally good
d) None of the mentioned

Answer: b [Reason:] B takes less time than A for the same task.

## Discrete Mathematics MCQ Set 4

1. The shaded area of figure is best described by a) A ∩ B
b) A U B
c) A
d) B

Answer: a [Reason:] The region is A intersection B.

2. The shaded area of figure is best described by a) A‘ (Complement of A)
b) A U B -B
c) A ∩ B
d) B

Answer: b [Reason:] The region is complement of B.

3. If n(A)=20 and n(B)=30 and n(A U B) = 40 then n(A ∩ B) is
a) 20
b) 30
c) 40
d) 10

Answer: d [Reason:] n(A U B) = n(A) + n(B) – n(A ∩ B).

4. The shaded area of figure is best described by a) A‘ (Complement of A)
b) B – (A ∩ B) – (C ∩ B)
c) A ∩ C ∩ B
d) B’ (Complement of B)

Answer: b [Reason:] The region is difference B with A and C.

5. The relation between sets A,B,C as shown by venn diagram is
a) A is subset of B and B is subset of C
b) C is not a subset of A and A is subset of B
c) C is subset of B and B is subset of A
d) None of the mentioned

Answer: c [Reason:] As set C is totally inside set B, set B is totally inside set A.

6. Let A : All badminton player are good sportsperson.
B: All person who plays cricket are good sportsperson.
Let X denotes set of all badminton players, Y of all cricket players, Z of all good sportsperson. Then which of the following statements is correct?
a) Z contains both X and Y
b) Z contains X and Y is outside
c) X contains Y and Z
d) None of the mentioned

Answer: a [Reason:] X and Y are subset of Z.

7. If n(A)=10 , n(B)=30,n(C)=50 and if set A,B,C are pairwise disjoint then which of the following is correct?
a) n(A U B)=0
b) n( B U C)=0
c) n( A U B U C)=90
d) All of the mentioned

Answer: d [Reason:] All the statements are true based on definition.

8. In the given figure the if n(A)=20,n(U)=50,n(C)=10 and n(A∩B)=5 then n(B)=? . a) 35
b) 20
c) 30
d)10

Answer: a [Reason:] Here n(B)= n(U) – n(A) + n(A∩B).

9. Let the students who likes table tennis be 12,the ones who like lawn tennis 10,those who like only table tennis are 6,then number of students who likes only lawn tennis are, assuming there are total of 16 students.
a) 16
b) 8
c) 4
d) 10

Answer: c [Reason:] The students who only plays lawn tennis will be total lawn tennis player – those who play both the sports.

10. The shaded area of figure is best described by a) A‘ (Complement of A)
b) A U B – (A ∩ B)
c) A – B
d) B

Answer: b [Reason:] The region is complement of( A intersection B).

## Discrete Mathematics MCQ Set 5

1. One’s complement in binary is defined as:
a) Flipping each binary bit
b) Adding one to the binary number
c) Flipping only bits having zero in it
d) None of the mentioned

Answer: a [Reason:] While taking 1’s complement we replace 1 with zero and vice versa.

2. What is the one’s complement of the number 1010110:
a) 1111111
b) 0101001
c) 1100110
d) None of the mentioned

Answer: b [Reason:] While taking 1’s complement we replace 1 with zero and vice versa.

3. One’s complement of a number x is y, then one’s complement of y is:
a) y
b) x
c) x + y
d) None of the mentioned

Answer: b [Reason:] Complement of Complement of number gives the same number.

4. Nine’s complement of a number is formed by:
a) replacing each digit by 9 minus that digit
b) replacing each digit by 1plus that digit
c) replacing each digit by 8 minus that digit
d) None of the mentioned

Answer: a [Reason:] Nine’s complement of a number is formed by replacing each digit by 9 minus that digit.

5. Radix complement can be obtained fromdiminished radix’s complement by:
a) Adding one to diminished radox’s complement
b) Subtracting one to diminished radox’s complement
c) Both are same things
d) None of the mentioned

Answer: a [Reason:] Radix complement = diminished radix complement +1.

6. State whether the given statement is true or false
In binary signed repersentation if most significant bit is one then that number is positive.
a) True
b) False

Answer: b [Reason:] In signed repersentation if most significant bit is one then that number is negative, for positive numbers msb = 0.

7. In signed representation 5 is represented in binary as 0101.
a) True
b) False

Answer: a [Reason:] Here msb is the signed bit which is zero, 101 evaluates to 5 hence it is +5.

8. The two’s complement of 101110100 is represented as?
a) 010001100
b) 101110101
c) 010001100
d) None of the mentioned

Answer: a [Reason:] 2’s complement = 1’s complement +1, 1’s complement = 010001011.

9. 9’s complement of 23456 is:
a) 87654
b) 76543
c) 12345
d) none of the mentioned