Programme Code : MCA Course Code : MCS-013 | More Year : 2012 Views: 1333 Submitted By : Monika On 20th September, 2012 Q. a) Make truth table for followings: i) ~p→(q ГҜғҡ r) ГҜғҷ p ГҜғҷ ~q ii) ~p→ ~r ГҜғҡ q ГҜғҷ ~p ГҜғҡ r b) What are conditional connectives? Explain use of conditional connectives with an example. c) Write down suitable mathematical statement that can be represented by the following symbolic properties. i) ( ГҜҖВӨ x) ( ГҜҖВў y) ( ГҜҖВў z) P ii) ГҜҖВӨ (x) ( ГҜҖВӨ y) ( ГҜҖВў z) P Question 2: Marks (3 + 3+3) a) What is proof? Explain method of direct proof with the help of one example. b) Show whether 11 is rational or irrational. c) Prove that A - (A - B) : A ГҜғҮ B Question 3: Marks (4 + 4+ 4) a) Set X has 10 members, how many members do P(X) has ? How many members of P(X) are proper subset of X ? b) Establish the equivalence: (P ГҜғВ  Q) ГҜғВ  (P ГҜғҷ Q) ГҜӮВә (~P + Q) ГҜғҷ (Q ГҜғВ  P) c) If p an q are statements, show whether the statement [(~p→q) ГҜғҷ (q)] → (p ГҜғҡ q) is a tautology or not. Question 4: Marks (4 + 3 +3) a) Make logic circuit for the following Boolean expressions: i) (x′.y + z) + (x+y+z)′ +(x+y.z) ii) ( x'+y).(y′+ z).(y.z′+x′) b) What is dual of a Boolean expression? Find dual of boolean expression of the output of the following logic circuit: c) Set A,B and C are: A = {1, 2, 3, 4, 5,6,9,19,15}, B = { 1,2,5,22,33,99 } and C { 2, 5,11,19,15}. Find the followings i. A - (A-B) ii. A ГҜғҲ BГҜғҲ C iii. A\B Question 5: Marks (4+4 +2) a) Draw a Venn diagram to represent followings: i) (A ГҜҒ„ B) ГҜғҲ (C ГҜғҲ B) ii) (AГҜҒ„B) ГҜғҮ (B ГҜҒ„C) b) Give geometric representation for following i) R x { 3} ii) {-1, -1) x (3, -3) c) Explain the concept of counterexample with the help of an example. Question 6: Marks (5+4) a) What is inclusion-exclusion principle? Explain inclusion-exclusion principle with an example. b) Find inverse of the following functions i) f(x) = 353ГҜҖВӯГҜҖВӯxx 3ГҜӮВ№x ii) f(x) = 4723ГҜҖВӯГҜҖВӯxx 2ГҜӮВұГҜӮВ№x Question 7: Marks (3 + 3 + 3) a) Find how many 3 digit numbers are even? How many 3 digit numbers are composed of odd digits. b) How many different 20 persons committees can be formed each containing at least 2 Professors and at least 3 Associate Professor from a set of 10 Professors and 42 Associate Professors. c) Prove that for every positive integer n, n3 + n is even. Question 8: Marks (4 +4 +2) a) What is DemorganГўҖҹs Law? Explain the use of DemorgenГўҖҹs law with an example? b) How many ways are there to distribute 10 district object into 4 distinct boxes with i) At least two empty box. ii) No empty box. c) In a fifty question true false examination a student must achieve twenty five correct answers to pass. If student answer randomly what is the probability that student will fail. No Answer Found

 Q write down suitable mathematical statement that can be represented by the following symbolic properties. JOYEETA PAUL    26th March, 2013 Hits: 1094