ExamBro
ExamBro
MHT CET · Maths · Sets and Relations

Let \(\mathrm{A}=[\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}], \mathrm{B}=[1,2,3]\). Relation \(\mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_4\) are as follows:
\(\mathrm{R}_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{c}, 1),(\mathrm{d}, 2)] \)
\(\mathrm{R}_2=[(\mathrm{a}, 1),(\mathrm{b}, 1),(\mathrm{c}, 1),(\mathrm{d}, 1)] \)
\(\mathrm{R}_3=[(\mathrm{a}, 2),(\mathrm{b}, 3),(\mathrm{c}, 2),(\mathrm{d}, 2)]\)
\(\mathrm{R}_4=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{a}, 2),(\mathrm{d}, 3)], \text { then }\)

  1. A only \(\mathrm{R}_3\) and \(\mathrm{R}_4\) are not functions
  2. B only \(R_1\) and \(R_2\) are not functions
  3. C only \(\mathrm{R}_3\) is not a function
  4. D only \(\mathrm{R}_4\) is not a function
Verified Solution

Answer & Solution

Correct Answer

(D) only \(\mathrm{R}_4\) is not a function

Step-by-step Solution

Detailed explanation

We find that in \(R_4, f(a)=1\) and \(f(a)=2\). Hence \(R_4\) is not a function.