Question

If $X = {x_1, x_2, x_3}$ and $Y = {x_1, x_2, x_3, x_4, x_5}$ then find which is a reflexive relation of the following ?

• A. $R_1 : {(x_1, x_1), (x_2, x_2)}$
• B. $R_1 : {(x_1, x_1), (x_2, x_2), (x_3, x_3)}$
• C. $R_3 : {(x_1, x_1), (x_2, x_2), (x_1, x_3),(x_2, x_4)}$
• D. $R_3 : {(x_1, x_1), (x_2, x_2),(x_3, x_3),(x_4, x_4)}$

Answer 1

Answer: (B)

$R_1 : {(x_1, x_1), (x_2, x_2), (x_3, x_3)}$

Answer 2

(a) Non-reflexive because $\left(x_{3}, x_{3}\right)\notin R_{1}$ (b) Reflexive (c) Non-Reflexive (d) Non-reflexive because $x_{4}\notin X$