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Which R is Not a Relation from A={1,2,3} to B={4,5,6} | JEE

JEE Maths question with a full step-by-step solution.

Question
If A={1,2,3}A = \{1, 2, 3\}, B={4,5,6}B = \{4, 5, 6\}, which of the following is not a relation from AA to BB?
AR1={(1,4),(1,5),(1,6)}R_1 = \{(1, 4), (1, 5), (1, 6)\}
BR2={(1,5),(2,4),(3,6)}R_2 = \{(1, 5), (2, 4), (3, 6)\}
CR3={(1,4),(1,5),(3,6),(2,6),(3,4)}R_3 = \{(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)\}
DR4={(4,2),(2,6),(5,1),(2,4)}R_4 = \{(4, 2), (2, 6), (5, 1), (2, 4)\}correct
Solution
A relation from AA to BB must satisfy R⊆A×BR \subseteq A \times B, i.e. first entry in A={1,2,3}A = \{1, 2, 3\} and second entry in B={4,5,6}B = \{4, 5, 6\}. In R4R_4: (4,2)(4, 2) has 4∉A4 \notin A, 2∉B2 \notin B, and (5,1)(5, 1) has 5∉A5 \notin A, 1∉B1 \notin B.
∴R4⊈A×B,\therefore R_4 \not\subseteq A \times B,
 so R4R_4 is not a relation from AA to BB. Correct answer: (4)
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