Relasi dan Fungsi [Part 3] - Banyak Pemetaan & Korespondensi satu satu

Summary

In this video, Pak Beni explains the concepts of mapping and one-to-one correspondence in functions. He starts by demonstrating how to calculate the number of possible mappings between two sets, using a clear formula involving the cardinality of the sets. He then introduces one-to-one correspondence, highlighting how it ensures every element in the domain has a unique pairing in the codomain. The video concludes with several examples and exercises, helping viewers solidify their understanding of these mathematical concepts, preparing them for future lessons on function notation.

Takeaways

• 😀 The video covers topics related to mappings, functions, and one-to-one correspondences between two sets.
• 😀 The goal of watching the video is to understand how to determine the number of mappings between two sets and the concept of one-to-one correspondence.
• 😀 A mapping is essentially a function that connects every element from one set (domain) to an element in another set (codomain).
• 😀 The number of possible mappings from set A to set B is determined using the formula: (number of elements in B) ^ (number of elements in A).
• 😀 In the example provided, set A has 3 elements and set B has 2 elements, so the number of possible mappings is 2^3 = 8.
• 😀 The concept of one-to-one correspondence (bijective function) is explained: each element in set A must correspond to a unique element in set B and vice versa.
• 😀 A function is not one-to-one if any element in the codomain (set B) does not have a unique partner in the domain (set A).
• 😀 One-to-one correspondence requires the number of elements in set A to be equal to the number of elements in set B.
• 😀 Several examples and exercises demonstrate how to apply the formula for finding the number of mappings and identify one-to-one correspondences.
• 😀 The video also discusses how to evaluate whether a given diagram or function is a one-to-one correspondence, using both set notation and visual representation.

Q & A

What is the main objective of the video?

The main objective of the video is to help viewers understand how to determine the number of possible mappings between two sets and to comprehend the concept of one-to-one correspondence in functions.

What is the formula for calculating the number of possible mappings from set A to set B?

The formula for calculating the number of possible mappings is given by: Number of mappings = |B|^|A|, where |A| is the number of elements in set A and |B| is the number of elements in set B.

How is the number of possible mappings between sets A and B demonstrated in the video?

In the video, Pak Beni demonstrates the number of possible mappings by showing how each element in set A can map to one of the elements in set B. For example, with set A = {2, 3, 4} and set B = {a, b}, the number of mappings is calculated as 2^3 = 8.

What is a one-to-one correspondence (korespondensi satu-satu) in the context of functions?

A one-to-one correspondence in functions refers to a situation where each element in set A is mapped to a unique element in set B, and vice versa, with no elements being left out or repeated.

How does the video differentiate between a regular function and a one-to-one correspondence?

The video differentiates the two by explaining that in a regular function, only the elements of set A need to be considered, whereas in a one-to-one correspondence, both sets, A and B, must have the same number of elements, and each element in A must correspond to a unique element in B.

In the example where set A = {1, 2, 3, 4} and set B = {a, b, c, d}, what makes this mapping a one-to-one correspondence?

This mapping is a one-to-one correspondence because each element in set A (1, 2, 3, 4) is mapped to exactly one unique element in set B (a, b, c, d), and all elements in both sets are involved.

How is the number of possible mappings calculated when set A has 3 elements and set B has 2 elements?

The number of possible mappings is calculated using the formula |B|^|A|. In this case, |A| = 3 and |B| = 2, so the number of possible mappings is 2^3 = 8.

What is the significance of the diagram used in the video to illustrate one-to-one correspondence?

The diagram helps visually identify one-to-one correspondences by showing arrows from elements in set A to set B. A one-to-one correspondence is indicated when each element in both sets has exactly one arrow linking to a unique counterpart in the other set.

What would disqualify a mapping from being a one-to-one correspondence in the examples shown in the video?

A mapping would be disqualified from being a one-to-one correspondence if any element in set A does not have a unique counterpart in set B, or if any element in set B remains unmatched. For example, if an element in set A is mapped to more than one element in set B, or if one element in set B has no partner, it is not a one-to-one correspondence.

What does Pak Beni emphasize about the relationship between the sizes of sets A and B in a one-to-one correspondence?

Pak Beni emphasizes that for a one-to-one correspondence to exist, the number of elements in set A must be equal to the number of elements in set B. This ensures that each element in one set can be paired with exactly one element in the other set.