Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words.
-$\left( B \cap C ^ { \prime } \right) \cup \left( C \cap B ^ { \prime } \right)$
A) All cola soda pops and all soda pops in cans
B) All non-cola soda pops not in cans
C) All cola soda pops not in cans or all non-cola soda pops in cans
D) All cola soda pops in cans and all non-cola soda pops not in cans

Question

Quizplus · Accepted Answer

The expression $\left( B \cap C ^ { \prime } \right) \cup \left( C \cap B ^ { \prime } \right)$ describes two groups: the first group, $B \cap C ^ { \prime }$, represents all cola soda pops that are not in cans (since $C ^ { \prime }$ denotes the complement of C, which includes all soda pops not in cans). The second group, $C \cap B ^ { \prime }$, represents all soda pops in cans that are not cola (since $B ^ { \prime }$ denotes the complement of B, which includes all non-cola soda pops). Therefore, the entire expression describes all cola soda pops not in cans or all non-cola soda pops in cans.

Let U = {All Soda Pops}, a = {All Diet (B∩C′)∪(C∩B′)\left( B \cap C ^ { \prime } \right) \cup \left( C \cap B ^ { \prime } \right)(B∩C′)∪(C∩B′)

Let U = {All Soda Pops}, a = {All Diet $\left( B \cap C ^ { \prime } \right) \cup \left( C \cap B ^ { \prime } \right)$