If A and B are two sets such that A ⊂ B, then what is A ∪ B?
If A and B are two sets such that A ⊂ B, then A ∪ B = B.
Explanation
The textbook provides a clear illustration in Example 13, where B ⊂ A and the result shows A ∪ B = A. The text explicitly states: 'This example illustrates that union of sets A and its subset B is the set A itself, i.e., if B ⊂ A, then A ∪ B = A.' By applying the same logic in reverse, when A ⊂ B, the union A ∪ B equals B because B already contains all elements of A. The union operation includes all elements from both sets, and since every element of A is already in B, the result is simply B.
Solution Steps
Step 1: Given A ⊂ B, which means every element of A is also an element of B.
Step 2: The union A ∪ B consists of all elements which are either in A or in B.
Step 3: Since all elements of A are already in B, A ∪ B = B.