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- I have a doubt, kindly clarify. - Sets, Relations and Functions - JEE Main-2
Let R be the set of real numbers.
Statement-1 : is an equivalence relation on R.
Statement-2 : is an equivalence relation on R.
- Option 1)
Statement-1 is true, Statement-2 is false.
- Option 2)
Statement-1 is false, Statement-2 is true.
- Option 3)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- Option 4)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Answers (1)
As we learnt in
Equivalence relation -
Any relation which is reflexive, symmetric and transitive is called an equivalence relation
-
A = {y - x is an integer}
B = {x = d, y}
A = {y - x is an integer for }
(a, a) it is an integer.
(a, b), (b, a) it is an integer
(a, b) (b, c) (a, c) it is an integer so that A is an equivalence relation.
Correct option is 1.
Option 1)
Statement-1 is true, Statement-2 is false.
This is the correct option.
Option 2)
Statement-1 is false, Statement-2 is true.
This is an incorrect option.
Option 3)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
This is an incorrect option.
Option 4)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
This is an incorrect option.
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