A) Statement-1 is false, Statement-2 is true
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
C) Statement-1 is true, Statement-2 is true Statement-2 is not a correct explanation for Statement-1
D) Statement-1 is true, Statement-2 is false
Correct Answer: D
Solution :
Statement-1 is true We observe that Reflexivity \[xRx\] as \[x-x=0\] is an integer, \[\forall x\in A\] Symmetric Let \[(x,y)\in A\] \[\Rightarrow y-x\] is an integer \[\Rightarrow x-y\]is also an integer Transitivity Let \[(x,y)\in A\] and \[(y,z)\in A\] \[\Rightarrow y-x\] is an integer and \[z-y\] is an integer \[\Rightarrow y-x+z-y\] is also an integer \[\Rightarrow z-x\] is an integer \[\Rightarrow (x,z)\in A\] Because of the above properties A is an equivalence relation over R Statement 2 is false as 'B' is not symmetric on \[\mathbb{R}\] We observe that \[OBx\] as \[0=0.x\forall x\in \mathbb{R}\] but \[(x,0)\notin B\]
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