The set {1,2,3,4,5} is equivalent to

Analysis

The question asks us to identify which set is "equivalent" to the set $\{1, 2, 3, 4, 5\}$. In set theory, two sets are considered equivalent if they have the exact same number of elements (the same cardinality).

Concept Explanation

• Equal Sets: Two sets are equal if they contain exactly the same elements, regardless of order. For example, $\{1, 2\}$ is equal to $\{2, 1\}$.
• Equivalent Sets: Two sets $A$ and $B$ are equivalent (written as $A \sim B$) if they have the same number of elements, meaning there is a one-to-one correspondence between them.
• Cardinality ($n$): The number of elements in a set. The set $\{1, 2, 3, 4, 5\}$ has 5 elements, so its cardinality $n = 5$.

Step-by-Step Solution

Let's count the number of elements in the given set and each of the options:

1. Given Set: $\{1, 2, 3, 4, 5\}$ has 5 elements.
2. Option A: $\{2, 3, 1, 4\}$ has 4 elements. (Not equivalent)
3. Option B: $\{1, 2, 3, 4, 5, 5\}$. In set theory, we do not count duplicate elements. This set is effectively $\{1, 2, 3, 4, 5\}$, which has 5 elements. However, in many JAMB contexts, "equivalent" is used to test the understanding of one-to-one mapping. Let's look at D.
4. Option C: $\{1, 2, 3, 4\}$ has 4 elements. (Not equivalent)
5. Option D: $\{4, 3, 1, 5, 2\}$ has 5 elements.

Comparing the options, Option D contains the exact same elements as the original set, just rearranged. While Option B contains the same values, the inclusion of a repeated '5' technically makes it the same set as the original, but Option D is a perfect mapping of the original set.

Exam Tip

When you see the word "equivalent" in a JAMB question, always count the number of elements first. If two sets have the same number of elements, they are equivalent. If they have the exact same elements, they are equal (and therefore also equivalent).