LA

Show that the relation $R$ defined in the set $A$ of all triangles as $R = \{(T_1, T_2) : T_1 \text{ is similar to } T_2\}$, is equivalence relation. Consider three right angle triangles $T_1$ with sides $3, 4, 5$, $T_2$ with sides $5, 12, 13$ and $T_3$ with sides $6, 8, 10$. Which triangles among $T_1, T_2$ and $T_3$ are related? [Competency]

VSA

Find the number of all onto functions from the set $\{1, 2, 3, \dots, n\}$ to itself. [NCERT]

VSA

Let $f:A\rightarrow B$ be defined by $f(x)=\frac{x-2}{x-3}$ where $A=R-\{3\}$ and $B=R-\{1\}$. Discuss the bijectivity of the function.

LA

If $N$ denotes the set of all natural numbers and $R$ is the relation on $N \times N$ defined by $(a, b) R (c, d)$ if $ad(b + c) = bc(a + d)$. Show that $R$ is an equivalence relation. [Delhi 2015, All India 2023]

VSA

Consider the relation $\phi$ on a non-empty set $A$. Then, check whether $R$ is symmetric, reflexive or transitive.

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