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Let P be the relation defined on the set of all real numbers such that P = {(a,b):sec2a − tan2b=1}.Then P is:
  • a)
    reflexive and symmetric but not transitive
  • b)
    reflexive and transitive but not symmetric
  • c)
    symmetric and transitive but not reflexive
  • d)
    an equivalence relation
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let P be the relation defined on the set of all real numbers such that...
Since the given function is reflexive.
sec2a − tan2b = 1 ∀x∈ R
For being symmetric,

To prove this,

                            = 1
Therefore, the function is symmetric.
For transitive,
sec2a − tan2b=1 ............. (2)
sec2b − tan2c=1 .......... (3)
Therefore, point P is reflexive, symmetric and transitive.’ Hence this is a equivalence relation.
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Most Upvoted Answer
Let P be the relation defined on the set of all real numbers such that...
This relation is not transitive.

To see why, consider the following counterexample:

Let a = π/4, b = π/3, and c = π/6.

Then (a,b) ∈ P because sec2a > sec2b,

and (b,c) ∈ P because sec2b > sec2c.

However, (a,c) ∉ P because sec2a < />

Therefore, the relation is not transitive.
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Let P be the relation defined on the set of all real numbers such that P = {(a,b):sec2a − tan2b=1}.Then P is:a)reflexive and symmetric but not transitiveb)reflexive and transitive but not symmetricc)symmetric and transitive but not reflexived)an equivalence relationCorrect answer is option 'D'. Can you explain this answer?
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Let P be the relation defined on the set of all real numbers such that P = {(a,b):sec2a − tan2b=1}.Then P is:a)reflexive and symmetric but not transitiveb)reflexive and transitive but not symmetricc)symmetric and transitive but not reflexived)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let P be the relation defined on the set of all real numbers such that P = {(a,b):sec2a − tan2b=1}.Then P is:a)reflexive and symmetric but not transitiveb)reflexive and transitive but not symmetricc)symmetric and transitive but not reflexived)an equivalence relationCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P be the relation defined on the set of all real numbers such that P = {(a,b):sec2a − tan2b=1}.Then P is:a)reflexive and symmetric but not transitiveb)reflexive and transitive but not symmetricc)symmetric and transitive but not reflexived)an equivalence relationCorrect answer is option 'D'. Can you explain this answer?.
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