# CLASS-7EQUIVALENT 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 XY.

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