Question

A function f is defined from R → R as f(x) = ax + b, such that f(1) = 1 and f(2) = 3. Find function f(x). Hence, check whether function f(x) is one-one and onto or not.

A relation R is defined on N × N (where N is the set of natural numbers) as : (a, b) R (c, d) ⇔ a – c = b – d. Show that R is an equivalence relation.

Assertion (A): The relation R = {(x, y) : (x + y) is a prime number and x, y ∈ N} is not a reflexive relation. Reason (R): The number '2n' is composite for all natural numbers n.

Let S be the relation defined by S = {(l₁, l₂) : l₁ is perpendicular to l₂}, check whether the relation S is symmetric and transitive.

A relation R is defined on a set of real numbers ℝ as R = {(x, y) : x · y is an irrational number}. Check whether R is reflexive, symmetric and transitive or not.