If A = {7, 8, 9} and B = {9, 5}, then (A `cup` B) x (A `cap` B) is

Options

A. {(7, 9), (7, 5), (8, 9), (8, 5), (9, 9), (9, 5)}
B. {(5, 9), (7, 9), (8, 9), (9, 9)}
C. {(9, 5), (9, 7), (9, 8), (9, 9)}
D. None of these

Answer

To solve the problem, we need to find the Cartesian product of the union and intersection of two sets A and B. Let's break it down step by step.

### Step 1: Identify the Sets
We are given:
- Set A = {7, 8, 9}
- Set B = {9, 5}

### Step 2: Find A Union B (A ∪ B)
The union of two sets includes all the elements from both sets, without duplicates.
- A ∪ B = {7, 8, 9} ∪ {9, 5}
- Combining these, we have: A ∪ B = {7, 8, 9, 5}

### Step 3: Find A Intersection B (A ∩ B)
The intersection of two sets includes only the elements that are present in both sets.
- A ∩ B = {7, 8, 9} ∩ {9, 5}
- The common element is: A ∩ B = {9}

### Step 4: Find the Cartesian Product (A ∪ B) × (A ∩ B)
The Cartesian product of two sets is the set of all ordered pairs (x, y) where x is from the first set and y is from the second set.
- We have A ∪ B = {7, 8, 9, 5} and A ∩ B = {9}
- Therefore, we will pair each element from A ∪ B with the single element from A ∩ B.

The ordered pairs will be:
1. (7, 9)
2. (8, 9)
3. (9, 9)
4. (5, 9)

Thus, (A ∪ B) × (A ∩ B) = {(7, 9), (8, 9), (9, 9), (5, 9)}

### Final Answer:
(A ∪ B) × (A ∩ B) = {(7, 9), (8, 9), (9, 9), (5, 9)}

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