Question

matching sets to a venn diagram
which of the following sets could be represented by the given venn diagram?
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}
s = {multiples of 4}
t = {8, 12, 20}

Explanation:

Step1: Analyze the Venn Diagram

The Venn diagram has two disjoint circles (no overlap), meaning sets \( S \) and \( T \) are disjoint (no common elements).

Step2: Check Each Option

• Option 1: \( S = \{ \text{Mercury, Venus, Earth, Mars} \} \), \( T = \{ \text{planets in our solar system} \} \). \( S \) is a subset of \( T \) (overlap), so not disjoint.
• Option 2: \( S = \{ \text{reptiles} \} \), \( T = \{ \text{mammals} \} \). Reptiles and mammals are disjoint (no common animals), so this fits.
• Option 3: \( S = \{ \text{prime numbers less than 10} \} = \{2, 3, 5, 7\} \), \( T = \{2, 3, 5, 7\} \). \( S = T \) (complete overlap), not disjoint.
• Option 4: \( S = \{ \text{multiples of 4} \} \), \( T = \{8, 12, 20\} \). \( T \) is a subset of \( S \) (overlap), so not disjoint.

Answer:

B. \( S = \{ \text{reptiles} \}, T = \{ \text{mammals} \} \) (assuming the second option is labeled B; if labels differ, adjust to the option with \( S = \{ \text{reptiles} \}, T = \{ \text{mammals} \} \))