# Discrete Mathematics One Mark Questions PREPARED BY:

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Discrete Mathematics One Mark Questions PREPARED BY:
R.RAJENDRAN. M.A., M. Sc., M. Ed., K.C.SANKARALINGA NADAR HR. SEC. SCHOOL, CHENNAI-21

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)

If a compound statement is made up of three simple statements, then the number of rows in the truth table is (a) (b) 6 (c) (d) 2 The number of rows in the truth table of [p٨(q)] is (a) (b) 4 (c) (d) 8

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) The conditional statement pq is equivalent to (a) p ٧ q (b) p ٧  q (c)  p ٧ q (d) p ٨ q

Which of the following is a tautology? (a) p ٧ q (b) p ٨ q (c) p ٧  p (d) p ٨  p Which of the following is a contradiction? (a) p ٧ q (b) p ٨ q (c) p ٧  p (d) p ٨  p

pq is equivalent to (a) p  q (b) q  p (c) (p q) ٧ (q  p) (d) (p q) ٨ (q  p) 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 =

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

In the set of integers with operation * defined by a * b = a + b – ab, the value of 3 * (4 * 5) is (a) (b) 15 (c) (d) 5 The order of [7] in (Z9, +9) is (a) 9 (b) 6 (c) (d) 1

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

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) (d) 50 The order of – i in the multiplicative group of 4th roots of unity is (a) 4 (b) 3 (c) (d) 1

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

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 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

The number of possible binary operation defined on a set with 5elements is (a) (b) 52 (c) (d) 5 The inverse of – 1 in the group (Z, +) is (a) 0 (b) – 2 (c) (d) 1

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 The value of [3] .5 [4] is (a) [0] (b) [4] (c) [1] (d) [2]

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

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 The value of [2] +8 [4] +8 [6] is (a) [0] (b) [2] (c) [3] (d) [4]

In the multiplication group of matrices of the form xR – {0}, the identity element is (a) (b) (c) (d) 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

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 (c) 2 and 3 (d) 4 only

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 (c) 3 and 4 (d) 4 only

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

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

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 (c) 1, 2 and 3 (d) 3 and 4

Which of the following are statements? (1) < (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

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

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

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

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

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 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

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

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 (c) 2, 3 and 4 (d) 3 and 4

‘+’ is not a binary operation on (a) N (b) Z (c) C (d) Q – {0} ‘–’ is a binary operation on (a) N (b) Q – {0} (c) R – {0} (d) Z

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

[5] .12 [11] is (a) [55] (b) [12] (c) [7] (d) [11] [3] +8 [7] is (a) [10] (b) [8] (c) [5] (d) [2]

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

In the group {G, }, G = {1, , 2},  is cube root of unity, order of 2 is (a) (b) (c) (d) 3 In the group {Z+, +4}, order of ([0]) is (a) (b)  (c) cannot be determined (d) 3

In the group {Z+, +4}, O([3]) is (a) 4 (b) 3 (c) 2 (d) 1 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

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 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

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 In {Z5 – {[0]}, 5), O([3]) is (a) 5 (b) (c) 4 (d) 2

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