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