DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > For real numbers a and b we write aRb if fa-b...
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For real numbers a and b we write aRb if f a - b + √2 is an irrational number. Then the relation R is :
- a)Reflexive
- b)Symmetric
- c)Both reflexive and symmetric
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For real numbers a and b we write aRb if fa-b+√2is an irrational...
Given that in the set of real numbers R,
aRb if f a - b + √2 is an irrational number
Reflexive : Reflexive relation on a set is a binary
element in which every element is related to itself.
x - x + √2 = √2 (irrational) for every x
So R is a reflexive relation.
Symmetric : Let a = √2, b = 1 so
a-b+ √2 = √2 - 1 + √2 = 2√2 - 1 which is an irrational number
For symmetric relation: (a, b) ∈ R which implies that
(b, a) ∈ R
So if (√2 , 1) ∈ R then (1, √2) should also belong to R
⇒ a = 1 , b = √2
a - b + √2 = 1- √2 + √2 = 1 which is not an irrational number
। = (1, √2) does not belong to R
So R is not symmetric relation.
aRb if f a - b + √2 is an irrational number
Reflexive : Reflexive relation on a set is a binary
element in which every element is related to itself.
x - x + √2 = √2 (irrational) for every x
So R is a reflexive relation.
Symmetric : Let a = √2, b = 1 so
a-b+ √2 = √2 - 1 + √2 = 2√2 - 1 which is an irrational number
For symmetric relation: (a, b) ∈ R which implies that
(b, a) ∈ R
So if (√2 , 1) ∈ R then (1, √2) should also belong to R
⇒ a = 1 , b = √2
a - b + √2 = 1- √2 + √2 = 1 which is not an irrational number
। = (1, √2) does not belong to R
So R is not symmetric relation.
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For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer?.
For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For real numbers a and b we write aRb if fa-b+√2is an irrational number. Then the relation R is :a)Reflexiveb)Symmetricc)Both reflexive and symmetricd)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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