Which of these sets are equivalent? 1. {a,n,n,e} 2. {a,n,n} 3. {a,n,n,l,e} 4. {n,a,n,l}

Two sets are considered equivalent (or equal) if they contain exactly the same elements, regardless of the order or repetition of elements. Let's analyze each set:

1. **Set 1: {a, n, n, e}** - This set contains the elements: {a, n, e}.
2. **Set 2: {a, n, n}** - This set contains the elements: {a, n}.
3. **Set 3: {a, n, n, l, e}** - This set contains the elements: {a, n, l, e}.
4. **Set 4: {n, a, n, l}** - This set contains the elements: {n, a, l}.

Now, let's compare the sets:
- **Set 1** contains the elements {a, n, e}.
- **Set 2** contains the elements {a, n}.
- **Set 3** contains the elements {a, n, l, e}.
- **Set 4** contains the elements {n, a, l}.

Clearly, none of the sets contain exactly the same elements. Thus, **none of the sets are equivalent** to each other.

Would you like more details or have any questions?

Here are some related questions to consider:
1. What does it mean for two sets to be equivalent?
2. Can a set have repeated elements?
3. How would you determine if two sets are subsets of each other?
4. What is the difference between equivalent sets and equal sets?
5. Can sets be equivalent if they have different numbers of elements?

**Tip:** Remember, in set theory, the order of elements doesn't matter, and duplicate elements are ignored when determining set equivalence.

Discover how to determine the equivalence of sets in this example comparing four sets: {a,n,n,e}, {a,n,n}, {a,n,n,l,e}, and {n,a,n,l}. Learn the key principles of set theory, focusing on the concept of equivalent sets where order and repetition of elements don't matter. Ideal for students in Grades 5-7.

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