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Question Bank For IA1_DSE(DSGT) Sr no. Question 1 The statement (p->q) v (q->p) is 2 Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ____________ Option1 Contradiction 6x + 9 Option2 Tautology 6x + 7 Option3 Contingent 6x + 6 Option4 none 6x + 8 3 What would be the conjunctive normal form of ~[(p v ~q) Λ ~r] (p v r) Λ (~p v q) (r v ~p) Λ (r v q) (q v r) Λ (~p v q) (p v q) Λ (~p v q) 2 Contradiction 3 none 4 10 4 8 4 The logic statement (~p Λ q)Λ(q -> p) is 5 How many are born at exactly same hour, minute and second among 1,00,000 6 Let the students who likes table tennis be 12, the ones who like lawn tennis 10, those who like only table tennis are 6, then number of students who likes only lawn tennis are, assuming there are total of 16 students. 7 A={1,2,3} B={3,5,6} & C={0,1,4,5,7,8} which of the following may be considered as universal set for all the three sets A,B & C? Marks 1 2 Tautology 1 Contingent 1 2 1 16 2 {0} {1,2,3,4,5,6,7,8, {0,1,2,3,4,5,6,7, {1,2,3,4,5,6,7,8, ....} 8,9,10} 9} 1 8 For the statement “If I come early then I can get a car”. Select correct contrapositive statement. 9 Following is not a type of Function If I cannot get a If I cannot If I can get a car None of above car then I come early then then I can come cannot come I cannot get a early Surjective Bijective Onto Trijective early car 10 Let A = {1, 2, 3, 4}, and let R ={(1, 2),(2, 3),(3, 4),(2, 1)}. Find the transitive closure of R. R={(1,1),(1,2), R={(1,1),(1,2), R={(1,1),(1,2), (1,3)(1,4),(2,1), (1,3)(1,4),(2,1), (1,3)(1,4),(2,2), (2,2),(2,3),(2,4), (2,2),(2,3),(2,4), (2,3),(2,4), (3,4)} (3,4),(4,3)} (3,4)} 11 If function f: A->B is both one-to-one and onto then f is called as ______ Surjective 12 What equation would you form for “the product of three consecutive numbers is divisible by 6 ” to proof by Mathematical Induction. 13 Equivalence Relation is ____________________ n(2n)(3n)=6m 14 If there is a bijection between two sets A and B then _______ 15 A relation is said to be _____if whenever xRy, yRz then we have xRz. 16 If A is a subset of B then _______ 17 How many friends must you have to guarantee that at least 4 of them will have birthdays in the same month? 18 If f(x)=x and g(x)= |x| then fog(-3.5) is----- Bijective 2 Injective Trijective n*m*p=6m none of above 1 n(n+1)(n+2) =6m 1 Reflexive, Irreflexive, Reflexive, Reflexive, Symmetric and Symmetric and Antisymmetric Symmetric and Transitive Transitive and Transitive Asymmetric Cardinality of A Cardinality of B Cardinality of B None of the is greater than is greater than is equal to A mentioned B A Anti symmetric Symmetric Transitive Reflexive 1 1 The cardinality The cardinality of A is greater of B is greater than B than A 48 49 Cardinality is same None of the mentioned 37 36 1 -3.5 fog does not exist None 19 Recursive Formula for defining numeric equation is called as____ Difference Equation Recurrence Relation Complex Equation Diffraction Equation 20 " The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________" reflective, symmetric and transitive irreflexive, symmetric and transitive neither reflective, nor irreflexive but transitive irreflexive and antisymmetric Speak truth. Are you interested in mathematics? The sky is blue. Arise, awake and stop not till the goal is reached TRUE FALSE none ambiguous {(1,4),(4,7), (7,4),(1,13)} {(1,4),(1,7), (1,13),(4,4), (4,7),(7,4), (7,7)} {(1,4),(1,7), (4,4),(4,7),(7,4), (7,7)} {(1,4),(1,7), (1,13),(4,4), (7,7)} 40 50 60 55 22 1 None 3.5 21 Which of these is statement? 1 1 1 1 2 2 23 Let A={1,4,7,13} , R={(1,4),(4,7),(7,4),(1,13)}. Find the transitive closure by Warshall’s algorithm. 24 In a group of 300 persons, 160 drink tea and 170 drink coffee, 80 of them drink both, How many persons do not drink either? 25 How many even 4 digit whole numbers are there? 2 1 1358 7250 4500 3600 1 26 Amit must choose a seven-digit PIN number and each digit can be chosen from 0 to 9. How many different possible PIN numbers can Amit choose? 27 An integer is called a nice integer if it is not divisible by any of the numbers 3; 5 or 7. How many nice integers are there between 1 and 500 (both included) ? 28 In a class, there are boy students and girl students. Two students are said to best friends if they are of the same gender as well as their birthday lies in the same month. What is the minimum number of students in the class which ensures that there are at least two students in the class who are best friends? 10000000 229 9900000 220 67285000 270 39654900 269 1 1 13 12 24 25 2