JEE Mains · Maths · STD 12 - 1. relation and function
Let \(N\) denote the set of all natural numbers. Define two binary relations on \(N\) as \(R_1 = \{(x,y) \in N \times N : 2x + y= 10\}\) and \(R_2 = \{(x,y) \in N\times N : x+ 2y= 10\} \). Then
- A Both \(R_1\) and \(R_2\) are transitive relations
- B Both \(R_1\) and \(R_2\) are symmetric relations
- C Range of \(R_2\) is \(\{1, 2, 3, 4\}\)
- D Range of \(R_1\) is \(\{ 2, 4, 8\}\)
Answer & Solution
Correct Answer
(C) Range of \(R_2\) is \(\{1, 2, 3, 4\}\)
Step-by-step Solution
Detailed explanation
Here, \({R_1} = \left\{ {\left( {x,y} \right) \in N \times N:2x + y = 10} \right\}\) \({R_2} = \left\{ {\left( {x,y} \right) \in N \times N:x + 2y = 10} \right\}\) For \({R_1};2x + y = 10\) and \(x,y \in N\) So, possible values for \(x\) and \(y\) are: \(x = 1,y = 8\) i.e.…
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