Assertion Reasoning Quiz

Assertion (A): The value of the greatest integer function \([-2.5]\) is \(-2\).

Reason (R): The greatest integer function \(f(x) = [x]\) yields the greatest integer that is less than or equal to \(x\).

Assertion (A): The relation \(R = \{(x, y) : y = x^2, x \in \mathbb{R}\}\) represents a function from \(\mathbb{R}\) to \(\mathbb{R}\).

Reason (R): For every real number \(x\), there is a unique real number representing its square.

Assertion (A): For every relation from a set \(A\) to a set \(B\), its range is a subset of its codomain.
Reason (R): The domain of a relation is the set of all first components of its ordered pairs.

Assertion (A): The range of the fractional part function \(f(x) = x - [x]\) is the half-open interval \([0, 1)\).

Reason (R): The function \(g(x) = [x]\) (greatest integer function) always outputs integer values, making its range the set of integers \(\mathbb{Z}\).

Assertion (A): The range of the constant function \(f(x) = 5\) for all real \(x\) is the singleton set \(\{5\}\).

Reason (R): A constant function \(f(x) = c\) maps all elements of its domain to the same single constant value \(c\).