If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?

If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?

Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {1, 2, 3, 4}.
Step 2: Find the union of sets A and B, which is A ∪ B. This means we combine all unique elements from both sets.
Step 3: List the elements in A ∪ B. The unique elements are {1, 2, 3, 4}.
Step 4: Count the number of elements in A ∪ B. There are 4 elements: 1, 2, 3, and 4.
Step 5: Use the formula for the number of subsets. The number of subsets of a set with n elements is 2^n.
Step 6: Since A ∪ B has 4 elements, calculate 2^4.
Step 7: Calculate 2^4, which equals 16. This is the total number of subsets of A ∪ B.

Union of Sets – Understanding how to combine two sets to form a new set that contains all unique elements from both sets.
Subsets – Knowing that the number of subsets of a set with n elements is given by 2^n.