LA

Check whether the relation S in the set of real numbers R defined by $S=\{(a,b)$: where $a-b+\sqrt{2}$ is an irrational number is reflexive, symmetric or transitive.

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]

LA

Show that a function $f:\mathbb{R}\rightarrow\mathbb{R}$ defined as $f(x)=\frac{5x-3}{4}$ is both one-one and onto.

LA

Let $A=R-\{5\}$ and $B=R-\{1\}$. Consider the function $f:A\rightarrow B$, defined by $f(x)=\frac{x-3}{x-5}$ Show that f is one-one and onto.

VSA

If $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation in set $A = \{1, 2, 3, 4\}$. Is the relation $R$ symmetric?

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