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Discrete MathematicsOne Mark Questions
PREPARED BY:R.RAJENDRAN. M.A., M. Sc., M. Ed.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21
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)
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 [p٨(q)] is
(a) 2 (b) 4
(c) 6 (d) 8
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 pq is equivalent to
(a) p ٧ q (b) p ٧ q
(c) p ٧ q (d) p ٨ q
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
Choose The Correct Answer
8. pq 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 =ab 22 ba
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) (Zn, +n) (b) (Z, +)
(c) (Z, .) (d) (R, +)
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 (Z9, +9) is
(a) 9 (b) 6
(c) 3 (d) 1
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]
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) 52
(c) 25 (d) 50
17. The order of – i in the multiplicative group of 4th roots of unity is
(a) 4 (b) 3
(c) 2 (d) 1
22 ba
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
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
Choose The Correct Answer
21. The number of possible binary operation defined on a set
with 5elements is
(a) 25 (b) 52
(c) 10 (d) 5
22. The inverse of – 1 in the group (Z, +) is
(a) 0 (b) – 2
(c) 2 (d) 1
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]
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
Choose The Correct Answer
27. If (G, *) is a group and a, bG, 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]
Choose The Correct Answer
29. In the multiplication group of matrices of the form
xR – {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
xx
xx
10
01
2/12/1
2/12/1
01
10
00
00
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
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
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
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
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
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
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
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
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
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
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) pq is true
(c) p q is false (d) pq is true
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 pq is a
tautology
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
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
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]
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]
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
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
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
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
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 {Z5 – {[0]}, 5), O([3]) is
(a) 5 (b) 3
(c) 4 (d) 2
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 am = 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 a2 = e) for each a G, then G is Abelian
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 a2 = e (equivalently a = a – 1 )
(c) If O(G) 4, then G is Abelian
(d) (a * b)2 = a2 * b2 for all a, b G G is Abelian