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BCA (H) 2nd semester (Sessional (Minor I) Examination, April 2014) Subject Name: Discrete Mathematical Structure Duration: 1:30 hr. Max Marks: 50 Section A Objective Type Questions 1. What is the meaning of complement in set theory? A. all the elements in the universal set that are not identical B. a set of elements that work well with a given set C. all the elements of a universal set that do not belong to a subset of it D. all the elements that are the opposite of the elements in a given set 2.What is the meaning of disjoint in set theory? A. two or more sets having no elements in common B. two or more sets that do not match C. sets that are in different universal sets D. sets that contain no elements 3. A relation defined in a non-empty set A, having n elements, has A. n Relation B. 2 Relation 2 C.n Relation D.2n2 Relation 4. If F(x)=X3 and g(x)=cos3x then fog isA.x3.cos3x B.cos 3x2 C.cos33x D.3 cos x3 5.Let Function f: R——>R is define as f(x)=2x3-1 then f-1isA.2x3+1 B.(2x)3+1 C.(1-2x)3 D.(1+x)1/3 5*2=10 2 Section-B Short Answer Type questions (any Four) (4*5=20) Q1. If A, B, C are any three sets, prove A-(B∩C) = (A-B) ∪ (A-C) Q2. If A={1,2}, B= {2,3}, then find AxB and BxA. Is AxB =BxA ? Q3.Show that the mapping f: R- R Defined by f(x)=ex, x belong to R is one-one, where R is the set of real numbers. Q4.if P= he is poor, q= he is laborious, then write down the following statement in symbols. a. It is false that he is not poor or is laborious. b. He is poor or is not poor and is laborious. Q5. Define a. Intersection of two sets b. Difference of two sets. Section- C (Long Answer Type questions (any 2) 10*2=20 Q1. Show that the relation R ={(a,b): a,b belong to I and a-b is divisible by 3} is an equivalence relation. Q2. Prove (A∩B) ∪( A∩B’)=A Q3. Let R1 And R2 be a relation on a set A represented by a matrices: MR1= 1 0 1 010 11 0 MR2= 0 0 1 00 0 101 Find the matrices represented the following (1) R1 ∪ R2 (ii) R1 ∩ R2