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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A) :A relation R on the set of complex number defined by Z1 R Z2 ⇔ Z1 − Z2 is real, is an equivalence relation.
Reason(R) :Reflexive and symmetric properties may not imply transitivity.
Assertion(A) :A relation R on the set of complex number defined by Z1 R Z2 ⇔ Z1 − Z2 is real, is an equivalence relation.
Reason(R) :Reflexive and symmetric properties may not imply transitivity.
- a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- c)Assertion is true but Reason is false.
- d)Assertion is false but Reason is true.
Correct answer is option 'A'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given follo...
Assertion and Reason Analysis:
Assertion and Reason questions require careful analysis of both the assertion and the reason provided. Let's break down the given assertion and reason to understand why option (A) is the correct choice.
Assertion:
A relation R on the set of complex numbers defined by Z1 R Z2 ⇔ Z1 - Z2 is real, is an equivalence relation.
Reason:
Reflexive and symmetric properties may not imply transitivity.
Detailed Explanation:
Equivalence Relation:
An equivalence relation must satisfy three properties: reflexive, symmetric, and transitive.
1. Reflexive Property:
For any complex number Z, Z R Z must be true. In this case, Z - Z = 0, which is a real number, hence reflexive property holds.
2. Symmetric Property:
If Z1 R Z2 is true, then Z2 R Z1 must also be true. Since subtraction of complex numbers is commutative, this relation is symmetric.
3. Transitive Property:
For transitivity, if Z1 R Z2 and Z2 R Z3 are true, then Z1 R Z3 must also be true. However, the reason mentions that reflexive and symmetric properties do not imply transitivity, which is correct in general. But in this specific case, the subtraction of complex numbers is such that transitivity is also satisfied.
Therefore, the given relation R is an equivalence relation because it satisfies all three properties despite the general statement that reflexive and symmetric properties may not imply transitivity. Hence, option (A) is the correct choice.
Assertion and Reason questions require careful analysis of both the assertion and the reason provided. Let's break down the given assertion and reason to understand why option (A) is the correct choice.
Assertion:
A relation R on the set of complex numbers defined by Z1 R Z2 ⇔ Z1 - Z2 is real, is an equivalence relation.
Reason:
Reflexive and symmetric properties may not imply transitivity.
Detailed Explanation:
Equivalence Relation:
An equivalence relation must satisfy three properties: reflexive, symmetric, and transitive.
1. Reflexive Property:
For any complex number Z, Z R Z must be true. In this case, Z - Z = 0, which is a real number, hence reflexive property holds.
2. Symmetric Property:
If Z1 R Z2 is true, then Z2 R Z1 must also be true. Since subtraction of complex numbers is commutative, this relation is symmetric.
3. Transitive Property:
For transitivity, if Z1 R Z2 and Z2 R Z3 are true, then Z1 R Z3 must also be true. However, the reason mentions that reflexive and symmetric properties do not imply transitivity, which is correct in general. But in this specific case, the subtraction of complex numbers is such that transitivity is also satisfied.
Therefore, the given relation R is an equivalence relation because it satisfies all three properties despite the general statement that reflexive and symmetric properties may not imply transitivity. Hence, option (A) is the correct choice.
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :A relation R on the set of complex number defined by Z1 R Z2 ⇔ Z1 − Z2 is real, is an equivalence relation.Reason(R) :Reflexive and symmetric properties may not imply transitivity.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :A relation R on the set of complex number defined by Z1 R Z2 ⇔ Z1 − Z2 is real, is an equivalence relation.Reason(R) :Reflexive and symmetric properties may not imply transitivity.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. 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 In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :A relation R on the set of complex number defined by Z1 R Z2 ⇔ Z1 − Z2 is real, is an equivalence relation.Reason(R) :Reflexive and symmetric properties may not imply transitivity.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :A relation R on the set of complex number defined by Z1 R Z2 ⇔ Z1 − Z2 is real, is an equivalence relation.Reason(R) :Reflexive and symmetric properties may not imply transitivity.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?.
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