Discrete Mathematics MCQ Set 1
1. Which of the following statement is a proposition?
a) Get me a glass of milkshake
b) God bless you!
c) What is the time now?
d) The only odd prime number is 2
Answer
Answer: d [Reason:] Only this statement has got the truth value which is false.
2. The truth value of given statement is
‘4+3=7 or 5 is not prime’.
a) False
b) True
Answer
Answer: b [Reason:] Compound statement with ‘or’ is true when either of the statement is true. Here the first part of statement is true, hence whole is true.
3. Which of the following option is true?
a) If the Sun is a planet, elephants will fly
b) 3 +2 = 8 if 5-2 = 7
c) 1 > 3 and 3 is a positive integer
d) -2 > 3 or 3 is a negative integer
Answer
Answer: a [Reason:] Hypothesis is false, thus the whole statement is true.
4. What is the value of x after this statement, assuming initial value of x is 5?
‘If x equals to one then x=x+2 else x=0’.
a) 1
b) 3
c) 0
d) 2
Answer
Answer: c [Reason:] If condition is false so value decided according to else condition.
5. Let P: I am in Bangalore. , Q: I love cricket. ; then q -> p(q implies p) is:
a) If I love cricket then I am in Bangalore
b) If I am in Bangalore then I love cricket
c) I am not in Bangalore
d) I love cricket
Answer
Answer: a [Reason:] Q is hypothesis and P is conclusion. So the compound statement will be if hypothesis then conclusion.
6. Let P:If Sahil bowls, Saurabh hits a century. ,Q: If Raju bowls , Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true?
a) Raju bowled and Sahil got out on first ball
b) Raju did not bowled
c) Sahil bowled and Saurabh hits a century
d) Sahil bowled and Saurabh got out
Answer
Answer: c [Reason:] Either hypothesis should be false or both (hypothesis and conclusion) should be true.
7. The truth value of given statement is
‘If 9 is prime then 3 is even’.
a) False
b) True
Answer
Answer: b [Reason:] The first part of statement is false, hence whole is true.
8. Let P: I am in Delhi. , Q: Delhi is clean. ; then q ^ p(q and p) is:
a) Delhi is clean and I am in Delhi
b) Delhi is not clean or I am in Delhi
c) I am in Delhi and Delhi is not clean
d) Delhi is clean but I am in Mumbai
Answer
Answer: a [Reason:] Connector should be ‘and’, that is q and p.
9. Let P: This is a great website, Q: You should not come back here.
Then ‘This is a great website and you should come back here.’ is best represented by:
a) ~P V ~Q
b) P ∧ ~Q
c) P V Q
d) P ∧ Q
Answer
Answer: b [Reason:] The second part of statement is negated, hence negation operator is used.
10. Let P: We should be honest., Q: We should be dedicated .,R: We should be overconfident.
Then ‘We should be honest or dedicated but not overconfident.’ is best represented by:
a) ~P V ~Q V R
b) P ∧ ~Q ∧ R
c) P V Q ∧ R
d) P V Q ∧ ~R
Answer
Answer: d [Reason:] The third part of statement is negated, hence negation operator is used, for (‘or’ –V) is used and for(’but’- ∧).
Discrete Mathematics MCQ Set 2
1. Let set A ={1, 2} and C be {3, 4} then A X B (Cartesian product of set A and B) is
a) {1, 2, 3, 4}
b) {(1, 3) ,(2, 4)}
c) {(1, 3) , (2, 4), (1, 4) , (2, 3) }
d) {(3, 1), (4, 1)}
Answer
Answer: c [Reason:] In set A X B :{ (c , d) |c ∈ A and d ∈ B}.
2. If set A has 4 elements and B has 3 elements then set n(A X B) is
a) 12
b) 14
c) 24
d) 7
Answer
Answer: a [Reason:] The total elements in n(A X B) = n(A) * n(B).
3. If set A has 3 elements then number of elements in A X A X A are
a) 9
b) 27
c) 6
d)19
Answer
Answer: b [Reason:] n(A X A X A) = n(A)* n(A)* n(A).
4. Which of the following statements regarding sets is false ?
a) A X B = B X A
b) A X B ≠ B X A
c) n(A X B) = n(A) * n(B)
d) All of the mentioned
Answer
Answer: a [Reason:] The Cartesian product of sets is not commutative.
5. If n(A X B) = n(B X A) = 36 then which of the following may hold true?
a) n(A)=2, n(B)=18
b) n(A)=9, n(B)=4
c) n(A)=6, n(b)=6
d) None of the mentioned
Answer
Answer: c [Reason:] n(A) should be equal to n(B) for n(A X B) = n(B x A).
6. If C = {1} then C X (C X C) = (C X C) X C the given statement is
a) True
b) False
Answer
Answer: b [Reason:] The Cartesian product is not associative, (C × C) × C = { ((1, 1), 1) } ≠ { (1,(1, 1)) } = C × (C × C).
7. Let the sets be A, B, C, D then (A ∩ B) X (C ∩ D) is equivalent to
a) (A X C) ∩ (B X D)
b) (A X D) U (B X C)
c) (A X C) U ( B X D)
d) None of the mentioned
Answer
Answer: a [Reason:] (A ∩ B) X (C ∩ D) = (A X C) ∩ (B X D) but in case of unions this is not true.
8. If A ⊆ B then A X C ⊆ B X C the given statement is
a) True
b) False
Answer
Answer: a [Reason:] Let an arbitrary element x ∈ A and y ∈ C, then x ∈ B (subset property), (x,y) ∈ AX C also (x,y) ∈ B X C. This implies A X C ⊆ B X C.
9. If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is
a) 1024
b) 2048
c) 512
d) 4096
Answer
Answer: d [Reason:] The A X B has 12 elements ,then the number of subset are 2 12 = 4096.
10. If set A X B=B X A then which of the following sets may satisfy
a) A={1, 2, 3} , B={1, 2, 3, 4}
b) A={1, 2} , B={2, 1}
c) A={1, 2, 3} , B={2, 3, 4}
d) None of the mentioned
Answer
Answer: b [Reason:] For set A X B = B X A ,this is possible only when set A = B.
Discrete Mathematics MCQ Set 3
1. {x: x is an integer neither positive nor negative} is
a) Empty set
b) Non- empty set
c) Finite set
d) Both b and c
Answer
Answer: d [Reason:] Set = {0} non-empty and finite set.
2. {x: x is a real number between 1 and 2} is an
a) Infinite set
b) Finite set
c) Empty set
d) None of the mentioned
Answer
Answer: a [Reason:] It is an infinite set as there are infinitely many real number between any two different real numbers.
3. Write set {1, 5, 15, 25,…} in set-builder form :
a) {x: either x=1 or x=5n, where n is a real number}
b) {x: either x=1 or x=5n, where n is a integer}
c) {x: either x=1 or x=5n, where n is an odd natural number}
d) {x: x=5n, where n is a natural number}
Answer
Answer: c [Reason:] Set should include 1 or an odd multiple of 5.
4. Express {x: x= n/ (n+1), n is a natural number less than 7} in roster form:
a) {1⁄2, 2⁄3, 4⁄5, 6⁄7}
b) {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7, 7⁄8}
c) {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7}
d) Infinite set
Answer
Answer: c [Reason:] n/(n+1) = 1/(1+1) = 1⁄2 and n>7.
5. Number of power set of {a, b}, where a and b are distinct elements.
a) 3
b) 4
c) 2
d) 5
Answer
Answer: b [Reason:] Power set of {a, b} = {∅, {a, b}, {a}, {b}}.
6. Which of the following is subset of set {1, 2, 3, 4}.
a) {1, 2}
b) {1, 2, 3}
c) {1}
d) All of the mentioned
Answer
Answer: d [Reason:] There are total 16 subsets.
7. A = {∅,{∅},2,{2,∅},3} ,which of the following is true.
a) {{∅,{∅}} ∈ A
b) {2} ∈ A
c) ∅ ⊂ A
d) 3 ⊂ A
Answer
Answer: c [Reason:] Empty set is a subset of every set.
8. Subset of the set A= { } is:
a) A
b) {}
c) ∅
d) All of the mentioned
Answer
Answer: d [Reason:] Every set is subset of itself and Empty set is subset of each set.
9. {x: x ∈ N and x is prime} then it is:
a) Infinite set
b) Finite set
c) Empty set
d) Not a set
Answer
Answer: a [Reason:] There is no extreme prime, number of primes is infinite.
10. Convert set {x: x is a positive prime number which divides 72} in roster form:
a) {2, 3, 5}
b) {2, 3, 6}
c) {2, 3}
d) {∅}
Answer
Answer: c [Reason:] 2 and 3 are the divisors of 72 which are prime.
Discrete Mathematics MCQ Set 4
1. Let the sequence be 1×2, 3×22, 5×23, 7×24, 9×25……… then this sequence is
a) An airthmetic sequence
b) A geometic progression
c) Airthmetico-geometric progression
d) None of the mentioned
Answer
Answer: c [Reason:] If a1, a2……… are in AP and b1, b2………. are in GP then a2b2, a2b2,……… are in AGP.
2. Let the sequence be 1×2, 3×22, 5×23, 7×24, 9×25……… then the next term of this AGP is given by:
a) 10×26
b) 10×27
c) 11×26
d) None of the mentioned
Answer
Answer: c [Reason:] Since here a1, a2……… are in AP and b1, b2………. are in GP then a2b2, a2b2,……… are in AGP thus an = 11 and bn = 26.
3. The sum of the first n natural numbers is given by:
a) n(n+1)/2
b) n(n-1)/2
c) n2(n+1)/2
d) None of the mentioned
Answer
Answer: a [Reason:] 1 + 2 + 3 + 4 +……n = (n/2)(1 + n) Since this is AP.
4. The sum of square of the first n natural numbers is given by:
a) n(n+1)(2n+1)/6
b) n(n-1)/2(2n+1)
c) n2(n+1)(2n+1)/6
d) None of the mentioned
Answer
Answer: a [Reason:] 12 + 22 + 32 + 42 +……n2 = n(1+n)(2n+1)/6.
5. The sum of cubes of the first n natural numbers is given by:
a) {n(n+1)/2}2
b) {n(n-1)/2}2
c) {n2(n+1)/2}2
d) None of the mentioned
Answer
Answer: a [Reason:] 13 + 23 + 33 + 43 +……+ n3 = {n(n+1)/2}2.
6. State whether the given statement is true or false
The series 1, 1, 1, 1, 1…….. is not an AGP.
a) True
b) False
Answer
Answer: b [Reason:] Since 1, 1, 1, 1, 1…….. is in Ap and in Gp as well, Therfore the given sequence is also a AGP.
7.If in a AGP the common ratio of GP is 1 then that sequence becomes a AP sequence.
a) True
b) False
Answer
Answer: a [Reason:] In AGP sequence if r = 1, then terms are ab,(a+d)b,(a+2d)b…. and so on thus it is AP with common differnce bd.
8. The sequence 1, 1, 1, 1, 1…. is :
a) Absolutely summable
b) Is not absolutely summable
c) Can’t say
d) None of the mentioned
Answer
Answer: b [Reason:] For limit n tending to infinitythe sum also tends to infinity and thus it is not summable.
9. Which of the following is a Triangular number series :
a) 1, 3, 6, 9, 12, 15…..
b) 1, 3, 6, 10, 15, 21……
c) 1, 6, 12, 18, 24…..
d) none of the mentioned
Answer
Answer: b [Reason:] In triangular number sequence ith term is previous term+i,with first term as 1.
10.Which of the following is a fibonacci series:
a) 0, 1, 2, 3, 4…….
b) 0, 1, 1, 2, 3, 5……
c) 10, 12, 14, 16…….
d) none of the mentioned
Answer
Answer: b [Reason:] Fibonacci series is formed by adding previous two term starting from 0 and 1.
Discrete Mathematics MCQ Set 5
1. The contrapositive of p → q is the proposition:
a) ¬p → ¬q
b) ¬q → ¬p
c) q → p
d) ¬q → p
Answer
Answer: b [Reason:] Definition of contrapositive.
2. The inverse of p → q is the proposition:
a) ¬p → ¬q
b) ¬q → ¬p
c) q → p
d) ¬q → p
Answer
Answer: a [Reason:] Definition of inverse.
3. The converse of p → q is the proposition:
a) ¬p → ¬q
b) ¬q → ¬p
c) q → p
d) ¬q → p
Answer
Answer: c [Reason:] Definition of converse.
4. What is the contrapositive of the conditional statement? “The home team misses whenever it is drizzling?”
a) If it is drizzling, then home team misses
b) If the home team misses, then it is drizzling
c) If it is not drizzling, then the home team does not misses
d) If the home team wins, then it is not drizzling
Answer
Answer: d [Reason:] q whenever p contrapositive is ¬q → ¬p.
5. What is the converse of the conditional statement “If it ices today, I will play ice hockey tomorrow.
a) “I will play ice hockey tomorrow only if it ices today.”
b) “If I do not play ice hockey tomorrow, then it will not have iced today.”
c) “If it does not ice today, then I will not play ice hockey tomorrow.”
d) “I will not play ice hockey tomorrow only if it ices today.”
Answer
Answer: a [Reason:] If p, then q has converse q → p.
6. What are the contrapositive of the conditional statement “I come to class whenever there is going to be a test.
a) “If I come to class, then there will be a test.”
b) “If I do not come to class, then there will not be a test.”
c) “If there is not going to be a test, then I don’t come to class.”
d) “If there is going to be a test, then I don’t come to class.”
Answer
Answer: b [Reason:] q whenever p, has contrapositive ¬q → ¬p.
7. What are the inverse of the conditional statement “ A positive integer is a composite only if it has divisors other than 1 and itself.”
a) “A positive integer is a composite if it has divisors other than 1 and itself.”
b) “If a positive integer has no divisors other than 1 and itself, then it is not composite.”
c) “If a positive integer is not composite, then it has no divisors other than 1 and itself.”
d) None of the mentioned
Answer
Answer: c [Reason:] p only if q has inverse ¬p → ¬q.
8. What are the converse of the conditional statement “When Raj stay up late, it is necessary that Raj sleep until noon.”
a) “If Raj stay up late, then Raj sleep until noon.”
b) “If Raj does not stay up late, then Raj does not sleep until noon.”
c) “If Raj does not sleep until noon, then Raj does not stay up late.”
d) “If Raj sleep until noon, then Raj stay up late.”
Answer
Answer: d [Reason:] Necessary condition for p is q has converse q → p.
9. What are the contrapositive of the conditional statement “Medha will find a decent job when she labour hard.”?
a) “If Medha labour hard, then she will find a decent job.”
b) “If Medha will not find a decent job, then she not labour hard.”
c) “If Medha will find a decent job, then she labour hard.”
d) “If Medha not labour hard, then she will not find a decent job.”
Answer
Answer: b [Reason:] The statement q when p has its contrapositive as ¬q → ¬p.
10. What are the inverse of the conditional statement “If you make your notes, it will be a convenient in exams.”
a) “If you make notes, then it will be a convenient in exams.”
b) “If you do not make notes, then it will not be a convenient in exams.”
c) “If it will not be a convenient in exams, then you did not make your notes.”
d) “If it will be a convenient in exams, then you make your notes
Answer
Answer: b [Reason:] If p then q has inverse ¬p → ¬q.
