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Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
(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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