(Second time posting this problem)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 every element in B' is also in A'.
Let's break down the problem into small steps:
Step 1: Start with the assumption that A is a subset of B (given).
Step 2: Recall that B' is the complement of B, which means it contains all elements that are not in B.
Step 3: Similarly, A' is the complement of A, containing all elements that are not in A.
Step 4: To prove that B' is a subset of A', we need to show that for any element x in B', x is also in A'.
Step 5: Let x be an arbitrary element in B'.
Step 6: Since x is in B', it means x is not in B (by definition of complement).
Step 7: Using the assumption that A is a subset of B, we know that if x is not in B, then x is also not in A.
Step 8: Therefore, x is in B' implies x is in A'.
Step 9: Since step 5 was arbitrary, we can conclude that every element in B' is also in A', proving that B' is a subset of A'.
In conclusion, by following the above steps, we have proved that if A is a subset of B, then B' is a subset of A'.