Use the sample space S defined as S=[E_(1),E_(2),E_(3),E_(4),E_(5),E_(6),E_(7),E_(8),E_(9),E_(10)] Given overline (A)=[E_(2),E_(3),E_(6),E_(8)] and overline (B)=[E_(1),E_(4),E_(6),E_(7)] What is A intersection bar (B) a) [E_(1),E_(4),E_(6)] b) [E_(6),E_(7),E_(10)] c) [E_(5),E_(9),E_(10)] d) [E_(1),E_(4),E_(7)]

The correct answer is a) $[E_{6}]$.<br /><br />To find the intersection of sets A and $\bar{B}$, we need to identify the elements that are common to both sets.<br /><br />Set A is defined as $\overline{A}=[E_{2},E_{3},E_{6},E_{8}]$, which means it contains the elements $E_{2}$, $E_{3}$, $E_{6}$, and $E_{8}$.<br /><br />Set $\bar{B defined as $\overline{B}=[E_{1},E_{4},E_{6},E_{7}]$, which means it contains the elements $E_{1}$, $E_{4}$, $E_{6}$, and $E_{7}$.<br /><br />To find the intersection of sets A and $\bar{B}$, we need to identify the elements that are present in both sets. In this case, the only element that is common to both sets is $E_{6}$.<br /><br />Therefore, the intersection of sets A and $\bar{B}$ is $[E_{6}]$.