MTH202 Midterm Solved Subjective Including 2011 Papers by Moaaz

Latest Solved subjective from Midterm Papers

May 18,2011

Lectures 1-22 Moaaz Siddiq Latest subjectives

Spring 2011

Q1. Check whether it is the function

f n n

 Chapter 15

Q2. If a relation of A and B are reflexive and transitive then shows that their intersection is reflexive and transitive.

Lecture 13 Solution is on Page 11

Q3. If -9,-6,3,….66 series then find its nth term.

Herea d d n Formula for arithemeticseries.

1) na a n d n n

n

n n n

Q4. Question no 4 : Marx (2)

If

a n

Find its first four series of sequence??

Q4. If relation R is transitive then shows that its inverse is also transitive???

Solution:

Suppose that the relation R on A is transitive. Let (a, b) ∈ R-1and (b, c) ∈ R-1. Then by definition of R-1, (b, a) ∈R and (c, b) ∈R. Now R is transitive, therefore if (c, b) ∈R and (b, a) ∈R then (c, a) ∈R. Again by definition of R-1, we have (a, c) ∈ R-1. We have thus shown that for all a, b, c ∈ A, if (a, b) ∈ R1and (b, c) ∈ R-1then (a, c) ∈ R-1. Accordingly R-1 is transitive

Q6. If set (A,B) relation R is (2 marks)

(2,3)(6,5)(5,4)

Find its domain and rang??

15,2

15,2 13,4 9,6 9,6 3,8 3,8 :5

3,8 for Q hereb a funtion for b ais Q a b b therefore Q Q Q Q Q Q Nowa band function for it is therefore Q Q No.3 {(1, ),(2, ),(2, ),(3, )} find the domain and range of the above relati

dom={1,2, on A 3} ran={x,y ns R y x y x

Q No.4

that same example in the 14th lecture.. R S M M

find the RoS and Ros

Solution:

1. 0
2. 0 1.1 1.1 0.0 1.0 1.0 0.1 1.1
3. 0 1.0 0.1 1.1 1.0 0.0 1.0 1.1 0.1
4. 0
5. 0 0.1 0.1 0.0 0.0 0.0 0.1 0.1

RoS

RoS 