VSA

If $A = \{1, 3, 5, 7\}$ and $B = \{1, 2, 3, 4, 5, 6, 7, 8\}$, then find the number of one-to-one functions from $A$ into $B$.

VSA

Let $R$ be the equivalence relation in the set $Z$ of integers given by $R = \{(a, b) : 2 \text{ divides } a - b\}$. Write the equivalence class $[0]$. [All India 2018]

SA

Let $f : R \to R$ be the function defined by $f(x) = \frac{1}{2 - \cos x}, \forall x \in R$. Then, find the range of $f$.

VSA

A function $f : A \to B$ defined as $f(x) = 2x$ is both one-one and onto. If $A = \{1, 2, 3, 4\}$, then find the set $B$. [All India 2024]

LA

Let $f, g : N - \{1\} \to N$ be functions defined by $f(a) = \alpha$, where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^\alpha$ divides $a$, and $g(a) = a + 1$, for all $a \in N - \{1\}$. Then, check whether the function $f + g$ is one-one or onto. [Competency]

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