Aspire Faculty ID #17544 · Topic: UGC NET Computer Science August 2024 (Paper II) · Just now
UGC NET Computer Science August 2024 (Paper II)

Consider the following relations on ${1,2,3,4}$. Which of the following relations are reflexive ?

(A)
$R_1={(1,1),(1,2),(2,1),(2,2),(3,4),(4,1),(4,4)}$

(B)
$R_2={(1,1),(1,2),(2,1)}$

(C)
$R_3={(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)}$

(D)
$R_4={(2,1),(3,1),(3,2),(4,1),(4,2),(4,3)}$

(E)
$R_5={(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)}$

Choose the correct answer from the options given below :


Solution

For a relation on ${1,2,3,4}$ to be reflexive, it must contain


$(1,1),(2,2),(3,3),(4,4)$


Check each:


$R_1$ → missing $(3,3)$ ✘


$R_2$ → missing $(3,3),(4,4)$ ✘


$R_3$ → contains $(1,1),(2,2),(3,3),(4,4)$ ✔


$R_4$ → missing all diagonal pairs ✘


$R_5$ → contains all $(1,1),(2,2),(3,3),(4,4)$ ✔


Thus reflexive relations:


$R_3$ and $R_5$

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