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CBSE - Class 12 > Mathematics > Relations and Functions Worksheets

Free CBSE - Class 12 Mathematics - Relations and Functions worksheets

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1.
Determine whether each of the following relations are reflexive, symmetric and transitive: (iv) Relation $R$ in the set $Z$ of all integers defined as $R = \{(x, y) : x – y$ is an integer\}$
2.
Determine whether each of the following relations are reflexive, symmetric and transitive: (v) Relation $R$ in the set $A$ of human beings in a town at a particular time given by (a) $R = \{(x, y) : x$ and $y$ work at the same place\}
3.
Determine whether each of the following relations are reflexive, symmetric and transitive: (v) Relation $R$ in the set $A$ of human beings in a town at a particular time given by (b) $R = \{(x, y) : x$ and $y$ live in the same locality\}
4.
Determine whether each of the following relations are reflexive, symmetric and transitive: (v) Relation $R$ in the set $A$ of human beings in a town at a particular time given by (c) $R = \{(x, y) : x$ is exactly 7 cm taller than $y\}$
5.
Determine whether each of the following relations are reflexive, symmetric and transitive: (v) Relation $R$ in the set $A$ of human beings in a town at a particular time given by (d) $R = \{(x, y) : x$ is wife of $y\}$
6.
Determine whether each of the following relations are reflexive, symmetric and transitive: (v) Relation $R$ in the set $A$ of human beings in a town at a particular time given by (e) $R = \{(x, y) : x$ is father of $y\}$
7.
Show that the relation $R$ in the set $R$ of real numbers, defined as $R = \{(a, b) : a \leq b^2\}$ is neither reflexive nor symmetric nor transitive.
8.
Let $L$ be the set of all lines in XY plane and $R$ be the relation in $L$ defined as $R = \{(L_1, L_2) : L_1$ is parallel to $L_2\}$. Show that $R$ is an equivalence relation. Find the set of all lines related to the line $y = 2x + 4$.
9.
Let $A = \{– 1, 0, 1, 2\}$, $B = \{– 4, – 2, 0, 2\}$ and $f, g : A \to B$ be functions defined by $f(x) = x^2 – x$, $x \in A$ and $g(x) = 2|\frac{x}{2} - 1| - 1$, $x \in A$. Are $f$ and $g$ equal? Justify your answer. (Hint: One may note that two functions $f : A \to B$ and $g : A \to B$ such that $f(a) = g(a) \forall a \in A$, are called equal functions).
10.

Let $A = \{1, 2, 3\}$. Then number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive is

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Chapters in CBSE - Class 12 Mathematics

Application of Derivatives Worksheet Application of Integrals Worksheet Continuity and Differentiability Worksheet Determinants Worksheet Differential Equations Worksheet Integrals Worksheet Inverse Trigonometric Functions Worksheet Linear Programming Worksheet Matrices Worksheet Probability Worksheet Three Dimensional Geometry Worksheet Vector Algebra Worksheet

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