Short Quiz

Assertion (A): If \((x+1,\,y-2)=(3,1)\), then \(x=2\) and \(y=3\).
Reason (R): In general, \(A\times B\neq B\times A\).

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): A school offers 4 clubs and 3 activity periods. If a student’s choice is recorded as ⟨club, period⟩, then there are 12 possible ordered choices.
Reason (R): Every club can be paired with each of the 3 activity periods.

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 \(c\).