Proving from Sets

  • MHB
  • Thread starter Albert1
  • Start date
  • Tags
    Sets
In summary, to prove that two sets are equal, you can either use the subset method or the element method. This is important because it allows us to use the sets interchangeably in mathematical operations. Even if two sets have different forms, they can still be proven to be equal as long as their elements are the same. Proving two sets are equal is related to the reflexive property, where we are essentially showing that both sets are equal to themselves. Additionally, the transitive property can also be used to prove that two sets are equal by showing that if A is equal to B and B is equal to C, then A is also equal to C.
  • #1
Albert1
1,221
0
Three sets given:

(1)

and

(2)

Prove:
 
Mathematics news on Phys.org
  • #2
Albert said:
Three sets given:

(1) and (2)
Prove:

Let's prove that In the same way, we could prove that
 
  • #3
Fernando Revilla said:
Let's prove that In the same way, we could prove that
Thanks! very good !
sol-1


sol-2


 
Last edited:

FAQ: Proving from Sets

How do you prove that two sets are equal?

To prove that two sets A and B are equal, you need to show that every element in set A is also in set B, and vice versa. This can be done by using the subset method, where you show that A is a subset of B and B is a subset of A. Alternatively, you can use the element method, where you show that every element in A is also in B and every element in B is also in A.

What is the importance of proving that two sets are equal?

Proving that two sets are equal is important because it allows us to show that they have the same elements, and therefore, they can be used interchangeably. This is especially useful in mathematics, where we often need to manipulate sets and perform operations on them.

Can you prove that two sets are equal if they have different forms?

Yes, two sets can still be proven to be equal even if they are in different forms. This is because the form of a set does not affect its elements. As long as you can show that all the elements in one set are also in the other, the sets can be considered equal.

What is the relationship between proving two sets are equal and the reflexive property?

The reflexive property states that every set is equal to itself. When we prove that two sets are equal, we are essentially showing that they are reflexive, or that they are equal to themselves. This is because we are showing that every element in one set is also in the other, which means that both sets are equal to themselves.

Can the transitive property be used to prove that two sets are equal?

Yes, the transitive property can be used to prove that two sets are equal. This property states that if A is equal to B and B is equal to C, then A is also equal to C. Therefore, if you can prove that set A is equal to set B and set B is equal to set C, then you can conclude that set A is also equal to set C.

Similar threads

Replies
4
Views
229
Replies
1
Views
1K
Replies
2
Views
3K
Replies
5
Views
1K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
1
Views
829
Back
Top