A) \[{{R}_{1}}=\{(x,y):y=x+2,x\in X,y\in Y\}\]
B) \[{{R}_{2}}=\{(1,1),(2,1),(3,3),(4,3),(5,5)\}\]
C) \[{{R}_{3}}=\{(1,1),(1,3),(3,5),(3,7),(5,7)\}\]
D) \[{{R}_{4}}=\{(1,3),(2,5),(2,4),(7,9)\}\]
Correct Answer: D
Solution :
[d] \[{{R}_{1}}\] is a relation from X to Y because \[{{R}_{1}}\subseteq X\times Y.\] \[{{R}_{2}}\] is a relation form X to Y because \[{{R}_{2}}\subseteq X\times Y.\] \[{{R}_{3}}\] is a relation from X to Y because \[{{R}_{3}}\subseteq X\times Y.\] \[{{R}_{4}}\] is not a relation form X to Y because (2, 4), (7, 9) \[\notin X\times Y.\]
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