This problem is related to Chapter-Sets. Please solve the question using x method. x method means x ∈ A ∩ B
Q. If A⊂B, then prove that B'⊂A'
To prove that B' is a subset of A', we need to show that any element in B' is also in A'.
First, let's define the concepts involved:
- A⊂B: This means set A is a subset of set B, which implies that every element in A is also in B.
- B': This is the complement of set B, also known as the set of all elements that are not in B.
- A': This is the complement of set A, or the set of all elements that are not in A.
Now, let's prove that B' is a subset of A':
Take any arbitrary element x∈B'. This means x is not in set B.
Since A⊂B, every element in set A is also in set B. Hence, if x is not in B, then x cannot be in A either.
Therefore, x∈B' implies x∈A'.
Thus, we have shown that any arbitrary element in B' is also in A'.
Hence, we can conclude that B'⊂A'.