UGC NET CSE | June 2016 | Part 2 | Question: 3

Question

Suppose that $R_1$ and $R_2$ are reflecive relations on a set A. Which of the following statements is correct?

• A. $R_1 \cap R_2$ is reflexive and $R_1 \cup R_2$ is irreflexive
• B. $R_1 \cap R_2$ is irreflexive and $R_1 \cup R_2$ is reflexive
• C. Both $R_1 \cap R_2$ and $R_1 \cup R_2$ are reflexive
• D. Both $R_1 \cap R_2$ and $R_1 \cup R_2$ are irreflexive

Answer 1

suppose we have A={a,b,c}

so reflexive relation must have  R1={(a,a),(b,b),(c,c)} all diagonal elements+ any thing

similarly R2=    {(a,a),(b,b),(c,c)} all diagonal elements+ any thing

so    R1 intersection R2 must have  {(a,a),(b,b),(c,c)}==>reflexive

and     R1 union  R2 must have  {(a,a),(b,b),(c,c)}==>reflexive

option 3 is correct