Let A and B be two sets having 5 and 7 elements respectively.write the minimum and maximum number of elemts in
(i) `A cup B`

Answer

To find the minimum and maximum number of elements in the union of two sets A and B, we can follow these steps:

### Step 1: Understand the Sets
Let:
- Set A has 5 elements.
- Set B has 7 elements.

### Step 2: Define the Union of Sets
The union of two sets A and B, denoted as \( A \cup B \), is the set containing all elements from both sets, without duplication.

### Step 3: Calculate Maximum Number of Elements in \( A \cup B \)
To find the maximum number of elements in \( A \cup B \):
- This occurs when there are no common elements between the two sets.
- Therefore, the maximum number of elements is the sum of the number of elements in both sets.

\[ \text{Maximum} = |A| + |B| = 5 + 7 = 12 \]

### Step 4: Calculate Minimum Number of Elements in \( A \cup B \)
To find the minimum number of elements in \( A \cup B \):
- This occurs when all elements of the smaller set (A) are also in the larger set (B).
- Thus, the minimum number of elements is equal to the number of elements in the larger set.

\[ \text{Minimum} = \max(|A|, |B|) = \max(5, 7) = 7 \]

### Final Answer
- Minimum number of elements in \( A \cup B \) = 7
- Maximum number of elements in \( A \cup B \) = 12

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