Question

matching sets to a venn diagram
which of the following sets could be represented by
the given venn diagram?
○ s = {multiples of 4}
t = {8, 12, 20}
○ s = {mercury, venus, earth, mars}
t = {planets in our solar system}
○ s = {reptiles}
t = {mammals}
○ s = {prime numbers less than 10}
t = {2, 3, 5, 7}

Explanation:

1. Analyze Option 1: \( S = \{\text{multiples of } 4\} \), \( T = \{8, 12, 20\} \). Since 8, 12, 20 are multiples of 4, \( T \) should be a subset of \( S \), but the Venn diagram shows disjoint sets, so this is incorrect.
2. Analyze Option 2: \( S = \{\text{Mercury, Venus, Earth, Mars}\} \), \( T = \{\text{planets in our solar system}\} \). The inner planets (S) are a subset of all solar system planets (T), but the diagram shows disjoint sets, so incorrect.
3. Analyze Option 3: \( S = \{\text{reptiles}\} \), \( T = \{\text{mammals}\} \). Reptiles and mammals are distinct groups (no overlap), matching the disjoint Venn diagram.
4. Analyze Option 4: \( S = \{\text{prime numbers less than } 10\} \), \( T = \{2, 3, 5, 7\} \). Here, \( T \) is equal to \( S \) (since prime numbers less than 10 are 2, 3, 5, 7), so they should coincide, not be disjoint. Thus, incorrect.

Answer:

C. \( S = \{\text{reptiles}\} \), \( T = \{\text{mammals}\} \)