Question

A relation R in = {1,2,3} is defined as = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which

element(s) of relation R be removed to make R an equivalence relation?​

Answer 1

Answer:

R is reflexive if it contains (1,1)(2,2)(3,3)

∵(1,2)∈R, (2,3)∈R

∴R is symmetric if (2,1),(3,2)∈R

Now, R={(1,1),(2,2),(3,3),(2,1),(3,2),(2,3),(1,2)}

R will be transitive if (3,1);(1,3)∈R. Thus, R becomes and

equivalence relation by adding (1,1)(2,2)(3,3)(2,1)(3,2)(1,3)(1,2). Hence,

the total number of ordered pairs is 7.