Math Problem Statement

Diketahui A = {1, 2, 3, 4, 5} dan B = {2, 4, 6}. Diagram panah yang merupakan relasi 'faktor dari' himpunan A ke himpunan B adalah?

Solution

The problem shows that sets A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\} and B={2,4,6}B = \{2, 4, 6\}, and it asks for the arrow diagram that represents the relation "faktor dari" (which translates to "factor of") from set AA to set BB.

To determine this, we need to understand the concept of "factor of". For an element in set AA to be related to an element in set BB, the element in AA must be a factor of the element in BB.

Checking for each element in set AA and its factors in set BB:

  • 1 is a factor of 2, 4, and 6.
  • 2 is a factor of 2, 4, and 6.
  • 3 is a factor of 6.
  • 4 is a factor of 4.
  • 5 is not a factor of any element in BB.

Now comparing this to the diagrams:

  • Option A correctly shows:
    • 1 connected to 2, 4, 6.
    • 2 connected to 2, 4, 6.
    • 3 connected to 6.
    • 4 connected to 4.
    • 5 not connected to any element.

Thus, the correct answer is Option A.

Would you like further details on how the factors are calculated?

Here are five related questions:

  1. How do you determine if one number is a factor of another?
  2. Can a number be a factor of itself?
  3. What is the significance of prime numbers in factorization?
  4. How are sets and relations represented in mathematical diagrams?
  5. What is the difference between a function and a relation?

Tip:

When dealing with sets and relations, always verify the conditions of the relation (such as "factor of") by applying them to each element individually to avoid mistakes.