집합과 명제 전체 문제

Let $A$, $B$, and $C$ be subsets of some universal set $U$.

Draw two general Venn diagrams for the sets $A$, $B$, and $C$. On one, shade the region that represents $A - \left( {B \cap C} \right)$, and on the other, shade the region that represents $\left( {A - B} \right) \cup \left( {A - C} \right)$. Based on the Venn diagrams, make a conjecture about the relationship between the sets $A - \left( {B \cap C} \right)$ and $\left( {A - B} \right) \cup \left( {A - C} \right)$.

Let $A$, $B$, and $C$ be subsets of some universal set $U$.

Draw two general Venn diagrams for the sets $A$, $B$, and $C$. On one, shade the region that represents $A - \left( {B - C} \right)$, and on the other, shade the region that represents $\left( {A - B} \right) - C$. Based on the Venn diagrams, make a conjecture about the relationship between the sets $A - \left( {B - C} \right)$ and $\left( {A - B} \right) - C$. (Are the two sets equal? If not, is one of the sets a subset of the other set?)

Let $A$, $B$, and $C$ be subsets of some universal set $U$.

Draw two general Venn diagrams for the sets $A$, $B$, and $C$. On one, shade the region that represents $A - \left( {B - C} \right)$, and on the other, shade the region that represents $\left( {A - B} \right) \cup \left( A - C^c \right)$. Based on the Venn diagrams, make a conjecture about the relationship between the sets $A - \left( {B - C} \right)$ and $\left( {A - B} \right) \cup \left( A - C^c \right)$. (Are the two sets equal? If not, is one of the sets a subset of the other set?)