Ques 1.

What is Set? Explain use of Set with examples

Ques 2.

Make truth table for followings. (4) i) p→(~r  q)  (~p  r) ii) p→ (~r  ~ q)  (p  ~ r)

Ques 3.

Give geometric representation for followings: (3) i) {5, -3) x ( -2, -2) ii) {-1, 3) x ( -2, 3)

Ques 4.

Draw Venn diagram to represent followings:  i) (A  B  C)  (A  B  C) ii) (A  B  C)  (B  C) iii) (A  B  C)

Ques 5.

Write down suitable mathematical statement that can be represented by the following symbolic properties. (4) i) (  x) (  y) (  z)P ii)  (z) (  y) (  z)Q

Ques 6.

Show whether √7 is rational or irrationl

Ques 7.

Explain use of inclusion-exclusion principle with example

Ques 8.

(b) Make logic circuit for the following Boolean expressions: (4) i) (xyz) + (xyz)' + (xz'y) ii) ( x'yz) (xyz') (xy'z)

Ques 9.

What is a tautology? If P and Q are statements, show whether the statement  (

Ques 10.

How many words can be formed using letter of “EXCELLENT” using each letter at most once?

Ques 11.

If each letter must be used,

Ques 12.

If some or all the letters may be omitted.

Ques 13.

What is a relation?What are different types of relation? Explain equivalence relation with the help of example.

Ques 14.

Prove that 12 +22+32+ …+ n2 = n(n+1)(2n+1)/6 ;  n ∈ N

Ques 15.

What is counterexample? Explain its use with the help of an example.

Ques 16.

How many different professionals committees of 8 people can be formed, each containing at least 2 Doctors, at least 2 Public Servants and 1 IT Expert from list of 7 Doctors, 6 Public Servants and 6 IT Experts?

Ques 17.

A and B are mutually exclusive events such that P(A) = 1/2 and P(B) = 1/3 and P (AU B) = 1/4. What is the probability of P(A Ո B)?

Ques 18.

Find how many 3 digit numbers are odd?

Ques 19.

Explain whether the function f(x) = x + 1 is one-one or not.

Ques 20.

How many ways are there to distribute 21 district items into 6 distinct boxes with: 
i) At least two empty box.
ii) No empty box.

Ques 21.

Explain principle of multiplication with an example.

Ques 22.

Three Sets A, B and C are: A = {1, 2,3,4,5, 8,9,12,15,17}, B = { 1,2, 3 ,4,8,9, 10 } and C {1,2,7, 9, 10, 11, 13}. Find A  B  C ; A  ~B  C; A  B  C and (A  ~C).

Ques 23.

Explain addition theorem in probability

Ques 24.

Make Pascal's triangle up to n = 6.

Ques 25.

What is a function? Explain different types of functions with example

Ques 26.

Write the following statements in symbolic form: 

(i) Mr. X is poor but happy.

(ii) Either eat healthy food or be ready for poor health.

Ques 27.

Find inverse of the following functions (3) f(x) = 3 2 3   x x x  3

Ques 28.

Find dual of Boolean Expression for the output ( Y) of the followinglogic circuit

Ques 29.

What is a proper subset ? Write the number of proper subsets of the Set {a, b, c, d, e, f}

Ques 30.

“If it rains, then you will play”. Write inverse and contrapositive for this sentence.