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Question
Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.
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Solution
Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = {(3, 8), (6, 6),(9, 4), (12, 2)}.
Explanation:
Given that, 2a + 3b = 30
3b = 30 – 2a
b = `(30 -2"a")/3`
= `10 - (2"a")/3`
Since 'a' and 'b' are natural numbers, 'a' must be multiple of '3'
For a = 3, b = 8
a = 6, b = 6
a = 9, b = 4
a = 12, b = 2
R = {(3, 8), (6, 6),(9, 4), (12, 2)}
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