Discrete Mathematics Set 3

Computer Science Engineering (CSE)

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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 3

Q1 | R is a relation defined in Z by aRb if and only if ab ³ 0, then R is
  • reflexive
  • symmetric
  • transitive
  • equivalence
Answer: equivalence
Q2 | Let a relation R in the set R of real numbers be defined as (a, b) Î R if and only if 1 + ab > 0 for all a, bÎR. The relation R is
  • reflexive and symmetric
  • symmetric and transitive
  • only transitive
  • an equivalence relation
Answer: reflexive and symmetric
Q3 | If R be relation ‘<‘ from A = {1, 2, 3, 4} to B = {1, 3, 5} ie, (a, b) Î R iff a < b, then RoR– 1 is
  • {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
  • {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
  • {(3, 3), (3, 5), (5, 3), (5, 5)}
  • { (3, 3), (3, 4), (4, 5)}
Answer: {(3, 3), (3, 5), (5, 3), (5, 5)}
Q4 | R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is
  • {(11, 8), (13, 10)}
  • {(8, 11), (10, 13)}
  • {(8, 11), (9, 12), (10, 13)}
  • none of the above
Answer: {(8, 11), (10, 13)}
Q5 | R is a relation on N given by N = {(x, y): 4x + 3y = 20}. Which of the following belongs to R?
  • (– 4, 12)
  • (5, 0)
  • (3, 4)
  • (2, 4)
Answer: (2, 4)
Q6 | The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given
  • {(1, 4), (2, 5), (3, 6), ….}
  • { (4, 1), (5, 2), (6, 3), ….}
  • {(4, 1), (5, 2), (6, 3), ….}
  • none of the above
Answer: { (4, 1), (5, 2), (6, 3), ….}
Q7 | Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
  • 7
  • 9
  • 10
  • 12
Answer: 7
Q8 | Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n (X ÇY) is equal to
  • 4
  • 6
  • 8
  • 12
Answer: 12
Q9 | Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the set A = { 3, 6, 9, 12 }. The relation is
  • reflexive and transitive
  • reflexive only
  • an equivalence relation
  • reflexive and symmetric only
Answer: reflexive and transitive
Q10 | Let f : ( - 1, 1 ) → B be a function defined by f ( x ) = 2 1 x 1 2x tan - - , then f is both one-one and onto when B is the interval
  • (0,π/2)
  • (0,(-π)/2)
  • (π/2,(-π)/2)
  • ((-π)/2,π/2)
Answer: ((-π)/2,π/2)
Q11 | Let R be the set of real numbers. If f : R → R is a function defined by f ( x ) = x2 , then f is]
  • inject ve but not subjective
  • subjective but not injective
  • bijective
  • none of these
Answer: none of these
Q12 | Which of the following statement is a proposition?
  • get me a glass of milkshake
  • god bless you!
  • what is the time now?
  • the only odd prime number is 2
Answer: the only odd prime number is 2
Q13 | What is the value of x after this statement, assuming the initial value of x is 5?‘If x equals to one then x=x+2 else x=0’.
  • 1
  • 3
  • 2
Q14 | Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is?
  • if i love cricket then i am in bangalore
  • if i am in bangalore then i love cricket
  • i am not in bangalore
  • i love cricket
Answer: if i love cricket then i am in bangalore
Q15 | 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?
  • raju bowled and sahil got out on first ball
  • raju did not bowled
  • sahil bowled and saurabh hits a century
  • sahil bowled and saurabh got out
Answer: sahil bowled and saurabh hits a century
Q16 | Let P: I am in Delhi.; Q: Delhi is clean.; then q ^ p(q and p) is?
  • delhi is clean and i am in delhi
  • delhi is not clean or i am in delhi
  • i am in delhi and delhi is not clean
  • delhi is clean but i am in mumbai
Answer: delhi is clean and i am in delhi
Q17 | 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?
  • ~p v ~q
  • p ∧ ~q
  • p v q
  • p ∧ q
Answer: p ∧ ~q
Q18 | 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?
  • ~p v ~q v r
  • p ∧ ~q ∧ r
  • p v q ∧ r
  • p v q ∧ ~r
Answer: p v q ∧ ~r
Q19 | The compound propositions p and q are called logically equivalent if                  is a tautology.
  • p ↔ q
  • p → q
  • ¬ (p ∨ q)
  • ¬p ∨ ¬q
Answer: p ↔ q
Q20 | p → q is logically equivalent to                  
  • ¬p ∨ ¬q
  • p ∨ ¬q
  • ¬p ∨ q
  • ¬p ∧ q
Answer: ¬p ∨ q
Q21 | p ∨ q is logically equivalent to                  
  • ¬q → ¬p
  • q → p
  • ¬p → ¬q
  • ¬p → q
Answer: ¬p → q
Q22 | ¬ (p ↔ q) is logically equivalent to
  • q↔p
  • p↔¬q
  • ¬p↔¬q
  • ¬q↔¬p
Answer: p↔¬q
Q23 | Which of the following statement is correct?
  • p ∨ q ≡ q ∨ p
  • ¬(p ∧ q) ≡ ¬p ∨ ¬q
  • (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
  • all of mentioned
Answer: all of mentioned
Q24 | p ↔ q is logically equivalent to                  
  • (p → q) → (q → p)
  • (p → q) ∨ (q → p)
  • (p → q) ∧ (q → p)
  • (p ∧ q) → (q ∧ p)
Answer: (p → q) ∧ (q → p)
Q25 | (p → q) ∧ (p → r) is logically equivalent to
  • p → (q ∧ r)
  • p → (q ∨ r)
  • p ∧ (q ∨ r)
  • p ∨ (q ∧ r)
Answer: p → (q ∧ r)
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