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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

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**Choose the Correct Answer**

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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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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 pq is equivalent to (a) p ٧ q (b) p ٧ q (c) p ٧ q (d) p ٨ q

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

pq 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 =

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**Choose The Correct Answer**

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, +)

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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]

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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]

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

In the multiplication group of matrices of the form xR – {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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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) pq is true (c) p q is false (d) pq is true

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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

‘+’ 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

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**Choose The Correct Answer**

‘’ 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]

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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

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**Choose The Correct Answer**

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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**Choose The Correct Answer**

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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THE END

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