Question

question 9 (1 point)
select all the sets equivalent to \\{\text{frog}, \text{toad}, \text{newt}, \text{snake}\\}

\\{3, z, 4, t\\}
\\{1, 2, 3, 5\\}
\\{\text{frog}, \text{toad}, \text{snake}\\}
\\{\text{apple}, \text{peach}, \text{pear}\\}
\\{\text{jim}, \text{bob}, \text{roy}\\}
\\{d, e, z, b\\}
\\{a, d, z, y, q\\}
\\{\text{femur}, \text{tibia}, \text{radius}, \text{ulna}\\}

Explanation:

🆕 New Concept Discovered: Equivalent Sets
Two sets are equivalent if they have the same number of elements.

Step 1: Count the elements in the given set

The given set is:

$$ S = \{\text{Frog}, \text{Toad}, \text{Newt}, \text{Snake}\} $$

Counting the elements:

1. Frog
2. Toad
3. Newt
4. Snake

The cardinality (number of elements) of the given set is:

$$ n(S) = 4 $$

For any other set to be equivalent to this set, it must also contain exactly 4 elements.

Step 2: Analyze each option

We check the number of elements in each of the provided choices:

• \( \{3, z, 4, t\} \): Contains 4 elements. (Equivalent)
• \( \{1, 2, 3, 5\} \): Contains 4 elements. (Equivalent)
• \( \{\text{Frog}, \text{Toad}, \text{Snake}\} \): Contains 3 elements. (Not equivalent)
• \( \{\text{apple}, \text{peach}, \text{pear}\} \): Contains 3 elements. (Not equivalent)
• \( \{\text{Jim}, \text{Bob}, \text{Roy}\} \): Contains 3 elements. (Not equivalent)
• \( \{d, e, z, b\} \): Contains 4 elements. (Equivalent)
• \( \{a, d, z, y, q\} \): Contains 5 elements. (Not equivalent)
• \( \{\text{Femur}, \text{Tibia}, \text{Radius}, \text{Ulna}\} \): Contains 4 elements. (Equivalent)

Answer:

The equivalent sets are:

• \( \{3, z, 4, t\} \)
• \( \{1, 2, 3, 5\} \)
• \( \{d, e, z, b\} \)
• \( \{\text{Femur}, \text{Tibia}, \text{Radius}, \text{Ulna}\} \)