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Discrete Mathematics One Mark Questions. Choose the Correct Answer 1. Which of the following statements are statements? (i) May God bless you (ii) Rose.

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Presentation on theme: "Discrete Mathematics One Mark Questions. Choose the Correct Answer 1. Which of the following statements are statements? (i) May God bless you (ii) Rose."— Presentation transcript:

1 Discrete Mathematics One Mark Questions

2 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)

3 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

4 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

5 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

6 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 =

7 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, +)

8 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) The order of [7] in (Z 9, + 9 ) is (a) 9(b) 6 (c) 3 (d) 1

9 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) The value of [3] + 11 ([5] + 11 [6]) is (a) [0](b) [1] (c) [2] (d) [3]

10 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) The order of – i in the multiplicative group of 4 th roots of unity is (a) 4(b) 3 (c) 2 (d) 1

11 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

12 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

13 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) The inverse of – 1 in the group (Z, +) is (a) 0(b) – 2 (c) 2 (d) 1

14 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]

15 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) (N,.) is a (a) group(b) semi group (c) monoid(d) abelian group

16 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]

17 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

18 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

19 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

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

21 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

22 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

23 Choose The Correct Answer 36. Which of the following are statements? (1) < 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

24 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) is an irrational number (3) Milk is white (4) The number 30 has four prime factors (a) TTTF (b) TTTT (c) TFTF (d) FTTT

25 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

26 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

27 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

28 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

29 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

30 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

31 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

32 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]

33 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]

34 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) In the group {G,  }, G = {1, – 1, i, – i }, order of – i is (a) 2 (b) 0 (c) 4 (d) 3

35 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) In the group {Z +, + 4 }, order of ([0]) is (a) 1 (b)  (c) cannot be determined (d) 3

36 Choose The Correct Answer 55. In the group {Z +, + 4 }, O([3]) is (a) 4 (b) 3 (c) 2(d) 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

37 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

38 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

39 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

40 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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