Let's break down the question step by step.
### (i) Number of Elements in Each Set
Given the sets:
- [tex]\( A = \{2, 4, 6, 8, 10\} \)[/tex]
- [tex]\( B = \{2, 3, 5, 7, 11\} \)[/tex]
To find the number of elements in each set, we simply count the elements within each set.
For set [tex]\( A \)[/tex]:
- The elements are 2, 4, 6, 8, and 10.
- Hence, the number of elements in [tex]\( A \)[/tex] is 5.
For set [tex]\( B \)[/tex]:
- The elements are 2, 3, 5, 7, and 11.
- Hence, the number of elements in [tex]\( B \)[/tex] is also 5.
So, the number of elements in each set is:
- [tex]\( A \)[/tex]: 5 elements
- [tex]\( B \)[/tex]: 5 elements
### (ii) Equality and Equivalence of Sets
#### Equality of Sets
Two sets are considered equal if they contain exactly the same elements.
Checking the elements of [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- [tex]\( A = \{2, 4, 6, 8, 10\} \)[/tex]
- [tex]\( B = \{2, 3, 5, 7, 11\} \)[/tex]
Clearly, the elements do not match. For example, 4 belongs to [tex]\( A \)[/tex] but not to [tex]\( B \)[/tex]; similarly, 3 belongs to [tex]\( B \)[/tex] but not to [tex]\( A \)[/tex].
Therefore, [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are not equal sets.
#### Equivalence of Sets
Two sets are considered equivalent if they have the same number of elements, regardless of what those elements are.
From part (i), both [tex]\( A \)[/tex] and [tex]\( B \)[/tex] have 5 elements.
Therefore, [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are equivalent sets.
### Conclusion
To summarize:
(i) The number of elements in each of the sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is 5.
(ii) [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are not equal sets, but they are equivalent sets as they have the same number of elements.
