If a set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
In mathematics, elements are the individual objects or members of a set. A set can contain numbers, letters, or other mathematical objects. For example, in the set A = {1, 2, 3}, the elements are 1, 2, and 3. Elements are denoted using curly brackets.
Class 12 Maths Relations and Functions Chapter 1 for CBSE Exam 2024-25 covers relations between sets and types of functions such as one-one and onto. Key topics include domain and range of functions composite functions and inverse functions. The chapter is essential for understanding higher-level mathematical concepts and further studies.
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In order to find the number of one-one and onto mappings or bijective functions from set A to set B, consider the following:
1. One-one mapping: Each element of A should map to a unique element of B.
2. Onto mapping: Every element of B should be associated with at least one element of A.
Observations:
Set A has 5 elements (|A| = 5), and set B has 6 elements (|B| = 6).
– For a bijection (one-one and onto), the no. of elements in both the sets must be equal, that is, |A| = |B|.
Now, |A| ≠ |B| hence it is not possible to have a one-one and onto mapping.
Conclusion:
The number of one-one and onto mappings from A to B is:
0.
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