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If R is a relation from a finite set A h...

If `R` is a relation from a finite set A having `m` elements to a finite set B having `n` elements then the number of relations from A to B is
a. `2^(m n)` b. `2^(m n)-1` c. `n^m` d. `m^n`

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To solve the problem, we need to determine the number of relations from a finite set A with m elements to a finite set B with n elements. ### Step-by-Step Solution: 1. **Understanding Relations**: A relation R from set A to set B is defined as a subset of the Cartesian product A × B. The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B. 2. **Finding the Size of the Cartesian Product**: The number of elements in the Cartesian product A × B is given by the product of the number of elements in A and the number of elements in B. Therefore, the number of elements in A × B is: \[ ...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
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