Let A,B
 be sets. Consider the following two statements:
(i) |A∪B|=|A−B|+|B|

(ii) |A∪B|=|A−B|+|A∩B|
Both statements are true	
Statement (i) is true; (ii) is false	
Statement (i) is false; (ii) is true	
Both statements are false

Let's carefully analyze both statements.

### Statement (i): 
\[
|A \cup B| = |A - B| + |B|
\]
Here, \(A - B\) refers to the elements in \(A\) that are not in \(B\). The right-hand side counts the elements in \(A - B\) and all of the elements in \(B\), but some elements of \(A \cap B\) are being counted twice: once in \(B\) and again in \(A \cup B\).

Therefore, this statement is **false**. The elements in the intersection are overcounted.

### Statement (ii): 
\[
|A \cup B| = |A - B| + |A \cap B|
\]
This is the correct way to count the elements in \(A \cup B\). It splits the union into:
- \(A - B\) (the elements in \(A\) but not in \(B\)),
- and \(A \cap B\) (the elements common to both \(A\) and \(B\)).

This counts each element exactly once, making this statement **true**.

### Conclusion:
- Statement (i) is false.
- Statement (ii) is true.

Thus, the correct answer is:
\[
\boxed{\text{Statement (i) is false; (ii) is true}}
\]

Would you like more details or further explanation?

### Related Questions:
1. How does the inclusion-exclusion principle apply to set theory?
2. What is the formula for the cardinality of the union of three sets?
3. How can we visually represent \(A \cup B\) and \(A \cap B\) using a Venn diagram?
4. What is the difference between \(A - B\) and \(B - A\)?
5. How do the properties of sets change when dealing with infinite sets?

#### Tip:
When working with sets, always ensure you're not double-counting elements, particularly those in the intersection.

Let A, B be sets. Consider the following two statements:
(i) |A∪B|=|A−B|+|B|
(ii) |A∪B|=|A−B|+|A∩B|
Both statements are true
Statement (i) is true; (ii) is false
Statement (i) is false; (ii) is true
Both statements are false

Learn how to evaluate set theory statements with a focus on union, difference, and intersection. Understand why the statement |A ∪ B| = |A − B| + |A ∩ B| is true, and the importance of the inclusion-exclusion principle. Suitable for high school students in Grades 9-12.

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