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]

SA

Let $A = \text{set of workers in a publication house}$. Let $a R b$, if and only if $a$ and $b$ tell lie ; $a, b \in A$. (i) Is $R$ symmetric relation? (ii) Is this relation an equivalence relation?

SA

Let $A = R - \{2\}$ and $B = R - \{1\}$, consider the function $f : A \to B$ defined by $f(x) = \frac{x - 1}{x - 2}$. Is $f$ one-one and onto? [All India 2019]

LA

Show that $f:R\rightarrow R$ defined as $f(x)=\frac{x}{\sqrt{1+x^{2}}}$ is one-one but not onto.

SA

Let R be a relation defined over N, where N is set of natural numbers, defined as "mRn if and only if m is a multiple of n, m, $n\in N$." Find whether R is reflexive, symmetric and transitive or not.

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