A) Both S and T are equivalence relations on R.
B) S is an equivalence relation on R but T is not.
C) T is an equivalence relation R but S is not.
D) Neither S nor T is an equivalence relation on R.
Correct Answer: C
Solution :
\[T=\{(x,y):x-y\in I\}\]as \[0\in I,\] T is a reflexive relation. If \[x-y\in I\Rightarrow y-x\in I\] \[\therefore \]T is symmetrical also. If \[x-y={{I}_{1}},\] and \[y-z={{I}_{2}}\] Then \[x-z=x-y+y-z\] and \[{{I}_{2}}+{{I}_{2}}\in I\] \[\therefore \]T is also transitive.You need to login to perform this action.
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