you roll a die with the sample space s = {1, 2, 3, 4, 5, 6}. you define a as {1, 3, 5}, b as {2, 3, 4, 5…

Explanation:

Step1: Recall definitions

Exhaustive events: Their union is the sample - space. Mutually exclusive events: They have no common elements.

Step2: Analyze A and B

$A={1,3,5}$, $B = {2,3,4,5,6}$. $A\cup B={1,2,3,4,5,6}=S$, but $A\cap B = {3,5}\neq\varnothing$, so not mutually exclusive.

Step3: Analyze A and C

$A={1,3,5}$, $C={4,5}$. $A\cup C={1,3,4,5}\neq S$, and $A\cap C = {5}\neq\varnothing$, so neither exhaustive nor mutually exclusive.

Step4: Analyze A and D

$A={1,3,5}$, $D={3,5,6}$. $A\cup D={1,3,5,6}\neq S$, and $A\cap D={3,5}\neq\varnothing$, so neither exhaustive nor mutually exclusive.

Step5: Analyze B and C

$B = {2,3,4,5,6}$, $C={4,5}$. $B\cup C={2,3,4,5,6}\neq S$, and $B\cap C={4,5}\neq\varnothing$, so neither exhaustive nor mutually exclusive.

Answer:

None of the given pairs are both exhaustive and mutually exclusive.