1. **State the problem:** We have sets $A = \{x, y, z, w\}$, $B = \{x, w\}$, $C = \{z, w\}$, and $D = \{z, w, t\}$. We need to determine which of the following subset relations are true: $$ C \subseteq A, \quad B \subseteq A, \quad A \subseteq B, \quad A \subseteq C, \quad B \subseteq D, \quad A \subseteq D, \quad D \subseteq A, \quad C \subseteq D, \quad B \subseteq C $$ 2. **Recall the definition of subset:** A set $X$ is a subset of set $Y$ (written $X \subseteq Y$) if every element of $X$ is also an element of $Y$. 3. **Check each statement:** - $C \subseteq A$? $C = \{z, w\}$ and $A = \{x, y, z, w\}$. Both $z$ and $w$ are in $A$, so **true**. - $B \subseteq A$? $B = \{x, w\}$ and $A = \{x, y, z, w\}$. Both $x$ and $w$ are in $A$, so **true**. - $A \subseteq B$? $A$ has elements $y$ and $z$ not in $B$, so **false**. - $A \subseteq C$? $A$ has $x$ and $y$ not in $C$, so **false**. - $B \subseteq D$? $B = \{x, w\}$ and $D = \{z, w, t\}$. $x$ is not in $D$, so **false**. - $A \subseteq D$? $A$ has $x$ and $y$ not in $D$, so **false**. - $D \subseteq A$? $D = \{z, w, t\}$ and $t$ is not in $A$, so **false**. - $C \subseteq D$? $C = \{z, w\}$ and $D = \{z, w, t\}$. Both elements of $C$ are in $D$, so **true**. - $B \subseteq C$? $B = \{x, w\}$ and $x$ is not in $C$, so **false**. 4. **Final answer:** The correct subset relations are: $$ C \subseteq A, \quad B \subseteq A, \quad C \subseteq D $$