Let \( \mathrm{U}=\{1,2,3,4,5,6,7\}, \mathrm{S}=\{1,3,4,5\} \) and \( \mathrm{T}=\{1,4,6,7\} \). List the elements of the following sets. \( \mathrm{S}^{\prime} \cap \mathrm{T} \)

To find the elements of the set \( \mathrm{S}^{\prime} \cap \mathrm{T} \), we first need to determine \( \mathrm{S}^{\prime} \), which is the complement of \( \mathrm{S} \) in \( \mathrm{U} \). The elements of \( \mathrm{U} \) are \( \{1,2,3,4,5,6,7\} \) and the elements of \( \mathrm{S} \) are \( \{1,3,4,5\} \). Therefore, the elements in \( \mathrm{S}^{\prime} \) (the complement of \( \mathrm{S} \) in \( \mathrm{U} \)) would be: \[ \mathrm{S}^{\prime} = \mathrm{U} \setminus \mathrm{S} = \{2, 6, 7\} \] Now, we find the intersection of \( \mathrm{S}^{\prime} \) and \( \mathrm{T} \): \[ \mathrm{T} = \{1, 4, 6, 7\} \] The elements of \( \mathrm{S}^{\prime} \) are \( \{2, 6, 7\} \), so we check for common elements with \( \mathrm{T} \): - \( 6 \in \mathrm{T} \) - \( 7 \in \mathrm{T} \) Thus, the intersection \( \mathrm{S}^{\prime} \cap \mathrm{T} \) contains the elements: \[ \mathrm{S}^{\prime} \cap \mathrm{T} = \{6, 7\} \] Finally, the result is: \[ \{6, 7\} \]