Discrete Mathematics

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


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


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


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


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, +)


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


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]


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


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


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


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


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]


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


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]


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


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


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


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



(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


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


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



(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



(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


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


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


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


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


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


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


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]


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]


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


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


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


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


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


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


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

Discrete Mathematics

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