LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

EQUIVALENT SET

__Equivalent Set__

**When two finite sets
with an equal number of members are called Equivalent Set. If the sets ‘X’ & ‘Y’ are equivalent then we can say that, “ X is equivalent to Y " and
that can be written as X****↔****Y.**

__Example–1)__** Let, Set ‘X’ =
{ 1, 2, 3, 4, 5 } & Set ‘Y’ = { x/x is a letter of the
word KOLKATA }**

**n(X) = 5, And
n(Y) = { K, O, L, A, T }, So, n(Y) = 5**

**So, we can say
that ‘X’ ****↔**** ‘Y’.**

__Example-2)__** ‘A’ = { 2, 3, 4, 5, 6, 7,8
} **

** And ‘B’ = { 0, 2, 4, 6, 8, 10 , 12 }**

**Here, n(A) = 7, n(B)
= 7,**

**So, ‘A’ ****↔**** ‘B’**

__Example–3)__

**Let, X = { x / x is
even natural number less than 9 }**

**Y = { x / x is odd
number more than 2 and less than 10 }**

**Ans.) X =
{ x / x is even natural number less than 9 }**

**
=> X = { x / x is even natural number less than 9, n < 9 }**

**
X = { 2, 4, 6, 8 }, n(X) = 4 **

**And, Y = { x / x is
odd number more than 2 and less than 10 }**

**=> Y = { x / x is
odd number more than 2 and less than 12, ****n ****ϵ**** N, 2 < n < 10 }**

**
Y = { 3, 5, 7, 9 }, n(Y) = 4**

**So, n(X) = n (Y) = 4, n(X) = n (Y)**

** So, ‘X’ ****↔**** ‘Y’**

__Example–4)__

**Let, A = { y / y is a letter of the word BISWAJEET }**

**And B = { y / y is a letter of the word HOSPITAL },
then prove that ****A
****↔****
B**

**Ans.) A = { y / y is a letter of the word
BISWAJEET }**

** => A = { B, I, S, W, A, J, E, T }**

**So, n(A) = 8**

**And, B = { y / y is a letter of the word HOSPITAL }**

**=> B = { H, O, S, P, I, T, A, L }**

**So, n(B) = 8**

**We can see that, n(A) =n(B) = 8 ,**

**So, n(A) = n(B)**

**So, it is proven that A ****↔**** ****B**