How does "x does not belong to B' but does belong to A' " prove B' is a subset of A'?neelakash said:Homework Statement
I have to prove that if A blis a subset of B then B' is a subset of A'.
Homework Equations
The Attempt at a Solution
I did:
Let x belongs to B but x does not belong to A
=>x does not belong to B' but x belongs to A'
Hence proved.
please tell me if I am correct.
You are correct.I was wrong in that arguement.How does "x does not belong to B' but does belong to A' " prove B' is a subset of A'?
In mathematics, "A⊂B" means that set A is a subset of set B, which indicates that all elements in set A are also present in set B.
The subset relation "A⊂B" can be proven by showing that every element in set A is also present in set B. This can be done through a direct proof, a proof by contradiction, or a proof by contrapositive.
The statement "A⊂B ⇒ B'⊂A" means that if set A is a subset of set B, then the complement of set B is a subset of the complement of set A. This is significant because it shows the relationship between the original sets and their complements.
No, the statement "A⊂B ⇒ B'⊂A" requires the use of two sets - A and B. This is because the statement is about the subset relation between two sets and their respective complements.
The statement "A⊂B ⇒ B'⊂A" is used in various areas of mathematics and science, such as in set theory, graph theory, and computer science. It is also used in proving theorems and solving problems related to subsets and complements of sets.