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समानांतर संबंध (Equivalence Relation)

संक्रामक गुण (Transitive Property) (correct)

परिवर्ती संबंध (Symmetric Relation)

परिवर्ती गुण (Reflexive Property)

परिवर्ती गुण (Symmetric Property)

असमानता गुण (Irreflexive Property)

समानांतर संबंध (Equivalence Relation)

परिवर्ती गुण (Reflexive Property) (correct)

संक्रामक गुण (Transitive Property)

समानांतर संबंध (Equivalence Relation)

परिवर्ती गुण (Symmetric Property) (correct)

निर्धारित गुण (Reflexive Property)

समानता का कोई गुण नहीं (Non-equivalence Relation) Signup and view all the answers

शून्य संबंध (Empty Relation) Signup and view all the answers

अगर (a1, a2) ∈ R, तो (a2, a1) ∈ R होना चाहिए। Signup and view all the answers

यदि (a1, a2) ∈ R और (a2, a3) ∈ R, तो (a1, a3) ∈ R होना चाहिए। Signup and view all the answers

संबंध R प्रतिकृति, समरूप और संक्रामक होना चाहिए। Signup and view all the answers

(3, 4) Signup and view all the answers

हर तत्व का अपने आप से संबंध होना चाहिए। Signup and view all the answers

Mathematical beauty is just as hard to define as the beauty in any other kind of art.
There isn't a permanent place for ugly mathematics in the world.
A relation from set A to set B is a subset of A × B.
A function is a special type of relation.
A relation R on set A is a subset of A×A.
A relation R is reflexive if for every a in A, (a, a) is in R.
A relation R is symmetric if, for any (a,b) in R, (b,a) is also in R.
A relation R is transitive if, for any (a,b), (b,c) in R, (a,c) is also in R.
A relation R is an equivalence relation if it is reflexive, symmetric, and transitive.
A relation R is a universal relation if every element in set A is related to every other element in set A.
A relation R is a void relation if there is no element in set A related to another element in set A.

An equivalence relation is a relation that is reflexive, symmetric, and transitive.
A relation R is reflexive if (a, a) ∈ R for all a in A.
A relation R is symmetric if (a, b) ∈ R ⇒ (b, a) ∈ R
A relation R is transitive if (a, b) ∈ R and (b, c) ∈ R ⇒ (a, c) ∈ R

Consider a set of students in class XII, and a set of students in class XI. A relationship can be established between students—such as "is a sibling of," "is older than" or "lives in the same town as".
A relationship R = {(a,b): a and b are siblings}, would be a void relation, since a student would not be considered a sibling of themselves in this context.
A relationship R' = {(a,b): a and b have the same height} would be a universal relation, as every student in the set A would have students in the set B that have the same height or a difference in height that falls below 3 feet.