If R = {(m, n) : m and n are integers, m2 + n2 ≤ 4} is a relation, then the range of R is:

If R = {(1, 2), (2, 3), (3, 4)} is a relation from set A = {1, 2, 3} to set B = {2, 3, 4, 5}, then what are the domain and codomain of R?

If f(x) = √x and g(x) = 1x2, then find the domain of (f + g)(x).

A relation R = {(a, b) : a, b ∈ ℤ and a2 + 3b2 ≤ 10} is defined on the set of integers ℤ. Find the range set of relation R.

The range of the relation R defined by R = {(x, x + 2) : x ∈ {0, 1, 2, 3, 4}} is given by:

Let A = {1, 2, 3} and B = {a, b}. A relation R from set A to set B is given by R = {(1, a), (2, a), (2, b)}. Find the matrix representation of relation R, where rows correspond to 1, 2, 3 in order and columns correspond to a, b in order.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: An equivalence relation defined on a set divides it into equivalence classes that are permitted to partially overlap as long as their union covers the entire set. Reason R: A partition of a set mandates that the set is divided into completely disjoint subsets where every element belongs to exactly one subset. In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A relation defined on a set qualifies as an equivalence relation if it successfully satisfies any two of the following fundamental properties: reflexive, symmetric, or transitive. Reason R: The mandatory criteria for an equivalence relation dictate that the relation must simultaneously be reflexive, symmetric, and transitive. In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: An anti-symmetric relation entirely forbids two-way connections, meaning that even identical elements cannot be related in both directions. Reason R: A symmetric relation requires that whenever one element is related to another, the reverse relationship must also exist. In the light of the above statements, choose the most appropriate answer from the options given below: