IF A = {1,2,3} and B = {2,4} , then `A cup B ` has 5 elements .

Answer

To solve the problem, we need to determine the number of elements in the union of sets A and B. We will follow these steps:

### Step 1: Identify the elements in sets A and B
- Set A = {1, 2, 3}
- Set B = {2, 4}

### Step 2: Find the intersection of sets A and B
- The intersection of two sets (A ∩ B) includes elements that are common to both sets.
- In this case, the common element is 2.
- Therefore, A ∩ B = {2}.

### Step 3: Count the number of elements in each set
- The number of elements in set A (|A|) is 3 (elements are 1, 2, 3).
- The number of elements in set B (|B|) is 2 (elements are 2, 4).
- The number of elements in the intersection (|A ∩ B|) is 1 (the element is 2).

### Step 4: Use the formula for the number of elements in the union of two sets
- The formula for the number of elements in the union of two sets is:
\[ |A ∪ B| = |A| + |B| - |A ∩ B| \]
- Substituting the values we found:
\[ |A ∪ B| = 3 + 2 - 1 \]

### Step 5: Calculate the number of elements in the union
- Performing the calculation:
\[ |A ∪ B| = 5 - 1 = 4 \]

### Conclusion
- Therefore, the number of elements in the union of sets A and B is 4, not 5. Hence, the statement that "A cup B has 5 elements" is false.

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