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2015 Question paper of year 2015 of BE second year IT of subject Discrete Mathematical Structure New CGPA patturn. Question paper

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Are you looking for the previous year question papers of Solapur University BE in information technology.feel free to download question papers from here.This is the original question paper of BE second year IT.

1. Write the correct answer from the options given below : [14 marks]
1) Determine whether or not each of the following is a partition of the set N of positive
a) [{n|n > 5}, {n|n < 5}] b) [{n|n > 6}, {1, 3, 5}, {2, 4}]
c) [{n|n2 > 11}, {n|n2 < 11}] d) None
2) Which of the following statements is false ?
a) (P? Q) ? (~P ? Q) ? (P ? ~Q) is equal to ~Q? ~P
b) (P? Q) ? (~P ? Q) ? (P ? ~Q) is equal to Q? P
c) (P? Q) ? (~P ? Q) ? (P ? ~Q) is equal to Q? (P ? ~Q)
d) (P? Q) ? (~P ? Q) ? (P ? ~Q) is equal to [(P? ~P) ? Q]? (P ? ~Q)
3) To show that the circuit corresponding to the Boolean expression
(P ? Q)? (~P ? Q)? (~P ? ~Q) can be represented using two logical gates, one
shows that this Boolean expression is equal to ~P ? Q. The circuit
corresponding to (P ?Q? R) ? (~P ?Q? R) ? (~P ? ~Q? ~R) computes the same
function as the circuit corresponding to
a) (P? Q)? ~R b) P? (Q ? R) c) ~P? (Q ? R) d) (P? ~Q)? R
4) A relation R on a set A is called a partial order iff it is
a) Reflexive b) Antisymmetric
c) Transitive d) All above
5) A function f : A ?B is bijective iff it is
a) injective b) surjective
c) one to one and onto d) none
6) Which one is the contrapositive of q?p ?
a) p?q b) ¬p? ¬q. c) ¬q? ¬p d) none of these
7) Each of the following defines a relation on the positive integers N : (1) "x is greater
than y". (3) x + y = 10 (2) "xy is the square of an integer". (4) x + 4y = 10. Determine
which of the relations are : reflexive
a) 1 b) 2 and 3 c) 4 d) none
8) Let A = Z + the set of positive integers. Define the relation R on A by aRb if and
only if a|b. R is
a) transitive b) asymmetric c) both d) none
9) Which of the following two sets are equal ?
a) A = {1, 2} and B = {1} b) A = {1, 2} and B = {1, 2, 3}
c) A = {1, 2, 3} and B = {2, 1, 3} d) A = {1, 2, 4} and B = {1, 2, 3}
10) A relation R on a set A is called an equivalence relation iff it is
a) Reflexive and symmetric b) Transitive
c) Both d) None
11) If B is a Boolean Algebra, then which of the following is true.
a) B is a finite but not complemented lattice
b) B is a finite, complemented and distributive lattice
c) B is a finite, distributive but not complemented lattice
d) B is not distributive lattice
12) Let L be a lattice. Then for every a and b in L which one of the following is correct ?
a) a? b = a ?b b) a? (b? c) = (a? b) ? c
c) a? (b ? c) = a d) a? (b? c) = b
13) Abelian group satisfies additional ___________ property than group.
a) transitive b) inverse c) identity d) commutative
14) Integral domain in _____________ have property with no zero deviser.
a) ring b) field c) chain d) none

2. Attempt any five questions : [20 marks]
1) Write the PCNF of P ? (P? Q).
2) Obtain the CNF of (P ? (P?Q))?Q.
3) Define properties of binary relations in a set.
4) Explain equality of set and proper set.
5) Show implication (P?Q)?Q?P? Q and of (P ? Q) ?(P?Q).
6) Show that (p?q) ? (q?p) is logically equivalent to p?q with truth table.

3. What is POSET ? Give procedure to draw Hasse diagram for powerset of S = {a, b, c}. [8 marks]

4. Attempt any 5 questions : [20 marks]
1) Definition lattice with GLB and LUB example.
2) P1 = 123 P2 = 123 P3 = 123 P4 = 123 P5 = 123 P6 = 123
123 213 321 132 231 312
Draw permutation and prepare table for (P, *).
3) Write note on Group code.
4) Let A = B = {a, b, c}. Consider the relation g = {(a, b), (b, c), (c, c)}. Is g one-to-one ?
Is g onto ? Why ? With example explain.
5) What are the different type of functions.
6) Which of the partially ordered sets in figures (a), (b) and (c) are lattices ? Justify
your answer.
5. Write algorithm to convert infix expression to polish Notation with example. [ 8 marks]

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