Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \}$, $Q = \{ 5,7,9,11,13,15 \}$, and $R = \{ 5,6,7,8 \}$.

$\mathrm { Q } ^ { \prime } \cap \left( \mathrm { N } ^ { \prime } \cap \mathrm { U } \right)$
A) $\{ 6,8,10,12,14 \}$
B) $\{ 5,7,9,11,13,15 \}$
C) $\{ 6,7,8,9,10,11 \}$
D) $\varnothing ; Q ^ { \prime }$ and $\left( N ^ { \prime } \cap U \right)$ are disjoint sets.

Question

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \}$, $Q = \{ 5,7,9,11,13,15 \}$, and $R = \{ 5,6,7,8 \}$.

$\mathrm { Q } ^ { \prime } \cap \left( \mathrm { N } ^ { \prime } \cap \mathrm { U } \right)$
A) $\{ 6,8,10,12,14 \}$
B) $\{ 5,7,9,11,13,15 \}$
C) $\{ 6,7,8,9,10,11 \}$
D) $\varnothing ; Q ^ { \prime }$ and $\left( N ^ { \prime } \cap U \right)$ are disjoint sets.

Quizplus · Accepted Answer

First, find the complements and intersections. $N' \cap U$ results in the set of elements in $U$ but not in $N$, which are $\{5,7,9,11,13,15\}$. This is exactly $Q$. Since $Q'$ is the complement of $Q$ in $U$, $Q'$ and $Q$ have no elements in common, making them disjoint sets.

Use These Sets to Find the Following U={5,6,7,8,9,10,11,12,13,14,15},M={5,7,9,11},N={6,8,10,12,14}\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \}U={5,6,7,8,9,10,11,12,13,14,15},M={5,7,9,11},N={6,8,10,12,14}

Use These Sets to Find the Following $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \}$