Let A = {2, 3, 5, 8} and B = {4, 27, 125, 512}, then which of the following are relations from A to B ? Give reasons for your answer.
(i) `R_(1) = {(2, 4), (3, 125), (8, 512)}`
(ii) `R_(2) = {(2, 125), (512, 8), (3, 27)}`
(iii) `R_(3) = {(2, 512), (3, 125), ( 4,3)}`
(iv) `R_(4) = {(2, 512), (3, 125), (3, 4)}`

Explanation

To determine which of the given sets are relations from set A to set B, we need to check if each relation is a subset of the Cartesian product \( A \times B \). The Cartesian product \( A \times B \) consists of all possible ordered pairs where the first element is from set A and the second element is from set B.

Given:
- Set \( A = \{2, 3, 5, 8\} \)
- Set \( B = \{4, 27, 125, 512\} \)

### Step-by-Step Solution:

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