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Discrete Mathematics One Mark Questions

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Choose the Correct Answer 1. Which of the following statements are statements? (i) May God bless you (ii) Rose is a flower (iii) Milk is white (iv) 1 is a prime number (a) (i), (ii), (iii)(b) (i), (ii), (iv) (c) (i), (iii), (iv)(d) (ii), (iii), (iv)

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Choose The Correct Answer 2. If a compound statement is made up of three simple statements, then the number of rows in the truth table is (a) 8 (b) 6 (c) 4 (d) 2 3. The number of rows in the truth table of [p ٨ ( q)] is (a) 2 (b) 4 (c) 6 (d) 8

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Choose The Correct Answer 4. If p is T and q is F, then which of the following have the truth value T? (i) p ٧ q(ii) p ٧ q (iii) p ٧ q (iv) p ٨ ( q) (a) (i), (ii), (iii)(b) (i), (ii), (iv) (c) (i), (iii), (iv)(d) (ii), (iii), (iv) 5. The conditional statement p q is equivalent to (a) p ٧ q(b) p ٧ q (c) p ٧ q(d) p ٨ q

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Choose The Correct Answer 6. Which of the following is a tautology? (a) p ٧ q(b) p ٨ q (c) p ٧ p(d) p ٨ p 7. Which of the following is a contradiction? (a) p ٧ q(b) p ٨ q (c) p ٧ p(d) p ٨ p

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Choose The Correct Answer 8. p q is equivalent to (a) p q(b) q p (c) (p q) ٧ (q p)(d) (p q) ٨ (q p) 9. Which of the following is not a binary operation on R? (a) a * b = ab(b) a * b = a – b (c) a * b = (d) a * b =

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Choose The Correct Answer 10. A monoid become a group if it also satisfies the (a) closure axiom(b) associative axiom (c) identity axiom(d) inverse axiom 11. Which of the following is not a group? (a) (Z n, + n )(b) (Z, +) (c) (Z,.) (d) (R, +)

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Choose The Correct Answer 12. In the set of integers with operation * defined by a * b = a + b – ab, the value of 3 * (4 * 5) is (a) 25(b) 15 (c) 10(d) 5 13. The order of [7] in (Z 9, + 9 ) is (a) 9(b) 6 (c) 3 (d) 1

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Choose The Correct Answer 14. In the multiplicative group of cube root of unity, the order of 2 is is (a) 4(b) 3 (c) 2(d) 1 15. The value of [3] + 11 ([5] + 11 [6]) is (a) [0](b) [1] (c) [2] (d) [3]

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Choose The Correct Answer 16. In the set of real numbers R, an operation * is defined by a * b =, then the value of (3 * 4) * 5 is (a) 5(b) 5 2 (c) 25(d) 50 17. The order of – i in the multiplicative group of 4 th roots of unity is (a) 4(b) 3 (c) 2 (d) 1

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Choose The Correct Answer 18. Which of the following is correct? (a) An element of a group can have more than one inverse. (b) If every element of a group is its own inverse, then the group is abelian. (c) The set of all 2 2 real matrices forms a group under matrix multiplication (d) (a * b) –1 = a –1 * b –1 for all a, b G

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Choose The Correct Answer 19. In the multiplicative group of nth roots of unity, the inverse of k is (k < n) (a) 1/k (b) – 1 (c) n – k (d) n/k 20. In the set of integers under the operation * defined by a*b = a + b – 1, the identity element is (a) 0(b) 1 (c) a (d) b

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Choose The Correct Answer 21. The number of possible binary operation defined on a set with 5elements is (a) 2 5 (b) 5 2 (c) 10 (d) 5 22. The inverse of – 1 in the group (Z, +) is (a) 0(b) – 2 (c) 2 (d) 1

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Choose The Correct Answer 23. Which one of the following is false? (a) (N, +) is a semi group(b) (N,.) is a monoid (c) (Z, *) is a group (d) the set of all even integers with usual addition is a group 24. The value of [3]. 5 [4] is (a) [0](b) [4] (c) [1] (d) [2]

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Choose The Correct Answer 25. If a binary operation * is defined by a * b = 3a – b, then the value of (2 * 3) * 4 is (a) 2(b) 3 (c) 4(d) 5 26. (N,.) is a (a) group(b) semi group (c) monoid(d) abelian group

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Choose The Correct Answer 27. If (G, *) is a group and a, b G, then the solution of the equation a * x = b is (a) a * b –1 (b) a –1 * b (c) b * a –1 (d) b –1 * a 28. The value of [2] + 8 [4] + 8 [6] is (a) [0](b) [2] (c) [3](d) [4]

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Choose The Correct Answer 29. In the multiplication group of matrices of the form x R – {0}, the identity element is (a) (b) (c) (d) 30. Which one of the following is not a binary operation on the set of integers (a) addition (b) subtraction (c) a * b = ab/3 (d) a * b = a + b + 1

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Choose The Correct Answer 31. Which of the following are statements? (1) Chennai is capital of Tamil nadu (2) The earth is a planet (3) Rose is a flower (4) Every triangle is an isosceles triangle (a) all (b) 1 and 3 (c) 2 and 3 (d) 4 only

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Choose The Correct Answer 32. Which of the following are not statements? (1) Three plus four is eight (2) The sun is a planet (3) Switch on the light (4) Where are you going? (a) 1 and 3 (b) 2 and 3 (c) 3 and 4 (d) 4 only

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Choose The Correct Answer 33. The truth values of the following statements are (1) Ooty is in Tamil nadu and 3 + 4 = 8 (2) Ooty is in Tamil nadu and 3 + 4 = 7 (3) Ooty is in Kerala and 3 + 4 = 7 (4) Ooty is in Kerala and 3 + 4 = 8 (a) FTFF (b) FFFT (c) TTFF (d) TFTF

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Choose The Correct Answer 34. The truth values of the following statements are (1) Chennai is in India or 2 is an integer (2) Chennai is in India or 2 is an irrational number (3) Chennai is in China or 2 is an integer (4) Chennai is in China or 2 is an irrational number (a) TFTF (b) TFFT (c) FTFT (d) TTFT

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Choose The Correct Answer 35. Which of the following are not statements? (1) All natural numbers are integers (2) A square has five sides (3) The sky is blue (4) How are you? (a) 4 only (b) 1 and 4 (c) 1, 2 and 3 (d) 3 and 4

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Choose The Correct Answer 36. Which of the following are statements? (1) 7 + 2 < 10 (2) The set of rational numbers is finite (3) How beautiful you are! (4) Wish you all success (a) 3 and 4 (b) 1 and 2 (c) 1 and 3 (d) 2 and 4

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Choose The Correct Answer 37. The truth values of the following statements are (1) All the sides of a rhombus are equal in length (2) 1 + 19 is an irrational number (3) Milk is white (4) The number 30 has four prime factors (a) TTTF (b) TTTT (c) TFTF (d) FTTT

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Choose The Correct Answer 38. The truth values of the following statements are (1) Paris is in France (2) sin x is an even function (3) Every square matrix is non-singular (4) Jupiter is a planet (a) TFFT (b) FTFT (c) FTTF (d) FFTT

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Choose The Correct Answer 39. Let p be “Kamala is going to school” and q be “There are twenty students in the class”. “Kamala is not going to school or there are twenty students in the class” stands for (a) p q (b) p q (c) ~ p (d) ~ p q

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Choose The Correct Answer 40. If p stands for the statement “Sita likes reading” and q stands for the statement “Sita likes playing”. “ Sita likes neither reading nor playing” stands for (a) ~ p ~ q (b) p ~ q (c) ~ p q (d) p q

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Choose The Correct Answer 41. If p is true and q is unknown then (a) ~ p is true (b) p (~ p) is false (c) p (~ p) is true (d) p q is true 42. If p is true and q is false then which of the following is not true? (a) ~ p is true (b) p q is true (c) p q is false (d) p q is true

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Choose The Correct Answer 43. Which of the following is not true? (a) Negative of a negation of a statement is the statement itself (b) If the last column of its truth table contains only T then it is tautology (c) If the last column of its truth table contains only F then it is contradiction (d) If p and q are any two statements then p q is a tautology

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Choose The Correct Answer 44. Which of the following are binary operations on R? (1) a * b = min{a, b} (2) a * b = max{a, b} (3) a * b = a (4) a * b = b (a) all (b) 1, 2 and 3 (c) 2, 3 and 4 (d) 3 and 4

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Choose The Correct Answer 45. ‘+’ is not a binary operation on (a) N (b) Z (c) C (d) Q – {0} 46. ‘–’ is a binary operation on (a) N (b) Q – {0} (c) R – {0} (d) Z

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Choose The Correct Answer 47. ‘ ’ is a binary operation on (a) N (b) R (c) Z (d) C – {0} 48. In congruence modulo 5, {x z / x = 5k + 2, k z} represents (a) [0] (b) [5] (c) [7] (d) [2]

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Choose The Correct Answer 49. [5]. 12 [11] is (a) [55] (b) [12] (c) [7] (d) [11] 50. [3] + 8 [7] is (a) [10] (b) [8] (c) [5] (d) [2]

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Choose The Correct Answer 51. In the group {G, }, G = {1, – 1, i, – i }, order of – 1 is (a) – 1 (b) 1 (c) 2 (d) 0 52. In the group {G, }, G = {1, – 1, i, – i }, order of – i is (a) 2 (b) 0 (c) 4 (d) 3

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Choose The Correct Answer 53. In the group {G, }, G = {1, , 2 }, is cube root of unity, order of 2 is (a) 2 (b) 1 (c) 4 (d) 3 54. In the group {Z +, + 4 }, order of ([0]) is (a) 1 (b) (c) cannot be determined (d) 3

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Choose The Correct Answer 55. In the group {Z +, + 4 }, O([3]) is (a) 4 (b) 3 (c) 2(d) 1 56. In (S, o), xoy = x, x, y S, then ‘o’ is (a) only associative (b) only commutative (c) associative and commutative (d) neither associative nor commutative

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Choose The Correct Answer 57. In (N, *), x * y = max{x, y} x, y N then (N, *) is (a) only closed (b) only semi group (c) only monoid (d) a group 58. The set of positive even numbers, with usual multiplication forms (a) a finite group (b) only a semi group (c) only a monoid (d) an infinite group

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Choose The Correct Answer 59. The set of positive even numbers, with usual addition forms (a) a finite group (b) only a semi group (c) only a monoid (d) an infinite group 60. In {Z 5 – {[0]}, 5 ), O([3]) is (a) 5 (b) 3 (c) 4 (d) 2

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Choose The Correct Answer 61. Which of the following statement is false? (G is a group) (a) For any element a G, O(a) = O(a – 1 ) (b) Let a G and O(a) = n, then a m = e m divides n, where m Z (c) If O(a) = 2 for each a G, then G is Abelian (a e) (d) If a = a – 1 (or a 2 = e) for each a G, then G is Abelian

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Choose The Correct Answer 62. Which of the following is not true? (a) If (G, *) is Abelian then O(G) = 4 (b) If G is of even order then there is an element ‘a’ different from e such that a 2 = e (equivalently a = a – 1 ) (c) If O(G) 4, then G is Abelian (d) (a * b) 2 = a 2 * b 2 for all a, b G G is Abelian

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