Previous Year Questions on Mappings

Mappings - Previous Year Questions

Previous Year Questions on Mappings

Previous year questions on Mappings highlight the importance of this concept in mathematics and its applications in diverse fields. Mappings, also known as functions, trace back to the work of mathematicians such as Leonhard Euler. They are crucial for understanding transformations, relationships between sets, and advanced topics in Abstract Algebra. Explore detailed notes in Mathematics Notes.

Vidyasagar University

2023-24 (CBCS)

No Questions

2021-22 (CBCS)

No Questions

2020-21 (CBCS)

No Questions

2019-20 (CBCS)

If \(f:A\to B\) and \(g:B\to C\) be two mappings such that \(g\circ f:A\to C\) is surjective, then show that \(g\) is surjective. [2]
If \(f:\mathbb{R}\to \mathbb{R}\) be an function defined by \(f(x)=x^{2},~x\in \mathbb{R}\). And suppose \(P=\set{x\in \mathbb{R}:0\leq x \leq 4}\). Find \( f^{-1}\left[f(P)\right]\). Is \( f^{-1}\left[f(P)\right]\) equal to \(P\)? [2]
Prove that there is a one-to-one correspondence between the sets \( (0,1) \) and \( [0,1] \). [2]
Prove that there is a one-to-one correspondence between the sets \( (0,1) \) and \( [0,1] \). [2]
Let \(S=\set{x\in \mathbb{R}: -1\lt x\lt 1 } \) and \(f:\mathbb{R}\to S\) be defined by \(f(x)=\frac{x}{1+|x|},~\forall x\in \mathbb{R}\). Show that \(f\) is a bijection and find \(f^{-1}\). [5]

2018-19 (CBCS)

Find \(f\circ g\), if \(f:\mathbb{R}\to \mathbb{R}\) is defined by \(f(x)=|x|+x,~\forall x\in \mathbb{R}\) and \(g:\mathbb{R}\to \mathbb{R}\) is defined by \(g(x)=|x|-x,~\forall x\in \mathbb{R}\). [2]
Let \(f:A\to B\) and \(P\subseteq A\). Prove that \(P\subseteq f^{-1}f(P)\). [2]
Let \(f:A\to B\) and \(S\subset A\). then show that \(S\subset f^{-1}\left[f(S)\right]\). If further \(f\) be one-to-one and onto, then prove that \( f^{-1}\left[f(S)\right]=S\). [2]

2017-18 (CBCS)

Let \(P=\set{n\in \mathbb{Z}: 0\leq n \leq 5 } \), \(Q=\set{n\in \mathbb{Z}: -5\leq n \leq 0 } \) be two sets. Prove that cardinality of two sets are equal. [2]
If \(X\) and \(Y\) are two non-empty sets and \(f:X\to Y\) be an onto mapping, then for any subsets \(A\) and \(B\) of \(Y\), prove that \(f^{-1}(A\cup B)=f^{-1}(A)\cup f^{-1}( B) \). [2]

FAQs

What is a mapping in mathematics?
A mapping, or function, is a relation that associates each element of one set with exactly one element of another set.
What are injections, surjections, and bijections?
Injections are one-to-one mappings, surjections are onto mappings, and bijections are both one-to-one and onto mappings.
Why are mappings important?
Mappings are essential for understanding transformations, calculus, and algebraic structures like groups and fields.
What is a domain and codomain?
The domain is the set of all input values, while the codomain is the set of potential output values for a mapping.
How are mappings used in Linear Algebra?
In Linear Algebra, mappings describe linear transformations between vector spaces. Learn more in Linear Algebra Notes.
What is an identity mapping?
An identity mapping maps each element of a set to itself.
Can mappings be represented visually?
Yes, mappings can be represented using arrow diagrams, graphs, or matrices.
What is the difference between mappings and relations?
While all mappings are relations, not all relations are mappings. Mappings require each input to have exactly one output.
How are mappings applied in computer science?
Mappings are used in algorithms, data structures, and database schema design.
What are some examples of mappings in real life?
Examples include coordinate systems, financial models, and transformations in graphics rendering.