집합의 뜻과 포함 관계

Let $A$, $B$, and $C$ be subsets of some universal set $U$. For each of the following, draw a general Venn diagram for the three sets and then shade the indicated region.

$B \cup C$

Let $A$, $B$, and $C$ be subsets of some universal set $U$. For each of the following, draw a general Venn diagram for the three sets and then shade the indicated region.

$A \cap \left( {B \cup C} \right)$

Let $A$, $B$, and $C$ be subsets of some universal set $U$. For each of the following, draw a general Venn diagram for the three sets and then shade the indicated region.

$\left( {A \cap B} \right) - C$

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

Draw a Venn diagram with $A \subseteq B$ and $B \subseteq C$. Does it appear that $A \subseteq C$?

Let $S$, $T$, $X$, and $Y$ be subsets of some universal set. Assume that

• (i) $S \cup T \subseteq X \cup Y$; - (ii) $S \cap T = \emptyset$; and - (iii) $X \subseteq S$.

Using assumption (i), what conclusion(s) can be made if it is known that $a \in T$?

Let $S$, $T$, $X$, and $Y$ be subsets of some universal set. Assume that

• (i) $S \cup T \subseteq X \cup Y$; - (ii) $S \cap T = \emptyset$; and - (iii) $X \subseteq S$.

Using assumption (ii), what conclusion(s) can be made if it is known that $a \in T$?