Q. 24.5( 6 Votes )
A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows: (x, y) R x is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.
Answer :
Relatively prime numbers are also known as co-prime numbers. If there is no integer greater than one that divides both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and14 are not as their greatest common divisor is two.
Given, (x, y) R x is relatively prime to y
Here,
2 is co-prime to 3 and 7.
3 is co-prime to 7 and 10.
4 is co-prime to 3 and 7.
5 is co-prime to 3, 6 and 7.
∴ R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6), (5, 7)}
Domain of relation R = {2, 3, 4, 5}
Range of relation R = {3, 6, 7, 10}
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