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A relation R in a set A is called universal relation, if
  • a)
    each element of A is related to every element of A
  • b)
    if no element of A isrelated to any element of A
  • c)
    if every element of A isrelated to one element of A
  • d)
    if one element of A isrelated to all elements of A
Correct answer is 'A'. Can you explain this answer?
Verified Answer
A relation R in a set A is called universal relation, ifa)each element...
A relation R in a set A is called universal relation, if each element of A is related to every element of A i.e:

R = A x A.
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A relation R in a set A is called universal relation, ifa)each element...
Explanation:

Universal relation is a relation that relates every element of a set A to every other element of the same set A. In other words, it is a relation that is defined over the entire set A.

There are four options given in the question and the correct answer is option A. Let's see why.

Each element of A is related to every element of A:

This means that if we take any two elements of the set A, they will be related to each other. In other words, there will be no pair of elements in A that are not related to each other. This is the definition of a universal relation, and hence option A is correct.

No element of A is related to any element of A:

This is the opposite of a universal relation. If this were the case, then no two elements in A would be related to each other, and hence option B is incorrect.

Every element of A is related to one element of A:

This means that for each element in A, there is at least one other element in A that is related to it. However, this does not mean that every element in A is related to every other element in A, and hence option C is incorrect.

One element of A is related to all elements of A:

This means that there is a single element in A that is related to all other elements in A. However, this does not mean that every element in A is related to every other element in A, and hence option D is incorrect.

Conclusion:

Hence, we can conclude that the correct answer to the question is option A, which states that a universal relation is one where each element of A is related to every other element of A.
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A relation R in a set A is called universal relation, ifa)each element of A is related to every element of Ab)if no element of A isrelated to any element of Ac)if every element of A isrelated to one element of Ad)if one element of A isrelated to all elements of ACorrect answer is 'A'. Can you explain this answer?
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A relation R in a set A is called universal relation, ifa)each element of A is related to every element of Ab)if no element of A isrelated to any element of Ac)if every element of A isrelated to one element of Ad)if one element of A isrelated to all elements of ACorrect answer is '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 A relation R in a set A is called universal relation, ifa)each element of A is related to every element of Ab)if no element of A isrelated to any element of Ac)if every element of A isrelated to one element of Ad)if one element of A isrelated to all elements of ACorrect answer is '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 A relation R in a set A is called universal relation, ifa)each element of A is related to every element of Ab)if no element of A isrelated to any element of Ac)if every element of A isrelated to one element of Ad)if one element of A isrelated to all elements of ACorrect answer is 'A'. Can you explain this answer?.
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