discrete mathematics one mark questions. choose the correct answer 1. which of the following...
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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
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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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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
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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
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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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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
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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, +)
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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
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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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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
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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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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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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
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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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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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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]
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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
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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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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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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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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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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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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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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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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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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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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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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
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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
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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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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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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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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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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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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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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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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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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
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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
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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
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