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Joint Family System in Pakistan Bad or Good

Thursday, December 13, 2012 Edit This
Joint Family System in Pakistan Bad or Good

Dr Abdul Qadeer Khan Interview with JehanPakistan Newspaper Hidden Truths - VUsolutions.com Urdu Columns Website

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MTH202 Assignment 2 solution

Monday, December 03, 2012 Edit This

solution of Q3 is on handouts page 147
..........
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 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 [COLOR=#0000FF !important]one to one[/COLOR] and it is not one to one. So, f has not inverse.



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 [COLOR=#0000FF !important]definition[/COLOR] 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 [COLOR=#0000FF !important]sequence[/COLOR] 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 [COLOR=#0000FF !important]equation[/COLOR] 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
.............................

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.

...................
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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