MTH202 2ND ASSINGMENT SOLUTION IDEA FALL 2012

On Thu, Nov 29, 2012 at 8:36 PM, Dream Queen <sangumriaz007@gmail.com> wrote:

MTH202 2ND ASSINGMENT SOLUTION IDEA NOV 31-11-12 FALL 2012 

Maximum Marks: 15 

Due Date: 03-12-12



Q#01: Let X = {1, 5, 9}, Y = {3, 4, 7}

Define f : X Y by f(1) = 4, f(5) = 7, f(9) = 4 

Marks = 2+2+1



Hint:

Chapter 16_Pg118.





(i) Is f one-one?



No, f is not one-to-one because all the elements of X are not mapped onto the Y elements. In X, 1 and 9 are mapped onto the same element 4 of Y. 



(ii) Is f onto?

It's also not a onto function because in Y, 3 is not img of any element of X.





(iii) Does inverse of f exist? 

No, f has not inverse because 

A function f(x) has an inverse function if and only if f(x) is one to one and it is not one to one. So, f has not inverse. 



http://math.ucsd.edu/~wgarner/math4c/tex...se_func...





Q#02: Let A = {a, b, c} and R = {(a, c), (b, b), (c, a)} be a relation on A.

Determine whether R is reflexive, Symmetric, Transitive and anti-symmetric, or not. 

Marks = 1+1+1+1

Solution:

Hint:

Chapter 12.



R is not reflexive.

Reason:

Because in R (a, a) and (c, c) are not exist. While in Reflexive Relation each element of A is must related to itself. So, in R is only (b, b) exist.



R is Symmetric.

Reason:

Because all the element of R are two ways. So, it's symmetric.



R is not Transitive.

Reason:

According to definition it should be must if a à b à c then a à c. so, it is not applying here.

R is not anti-symmetric.

Reason:

Because (c, a) & (a, c) ∈ R but c ≠ a





Q#03: Find the 36th term of the arithmetic sequence whose 3rd term is 7 and 8th term is 17. Marks 6





Solution:



If

First term = a

Common difference = d

3rd term num = n = 3

8th term num = n = 8



So,

7 = a + (3-1) d

7 = a +2d------- (1)



17 = a + (8-1) d

17 = a +7d------- (2)

And now we find

d = ?

a =?

For finding the value of 'd' we subtract equation 1st from 2nd



17 = a + 7d

7 = a + 2d

-----------------

10 = 5d

10/2 = d



d = 2



For finding the value of 'a', we put the value of 'd' in equation (1).



7 = a + 2d

7 = a + 2(2)

7 = a + 4

7- 4 = a

a = 3

We know that

So, the value of 36th term is

= 3 + (36-1) 2

= 3 + (35) 2

= 3+70

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