02 Sets and Set Operations Online Quiz Questions

Let $U=\{1,2,3,4,5\}$ and $A=\{1,4\}$. Which set is $A^c$ relative to $U$?

If $A=\{1,2,3\}$ and $B=\{3,4,5\}$, what is $A\cup B$?

Let $A=\{1,2,3,4\}$ and $B=\{3,4,5\}$. Select all true statements.

Let $A=\{2,4\}$ and $B=\{2,4,6\}$. Select all statements that are true.

True or false: For every set $A$, $\varnothing\subseteq A$.

True or false: The complement $A^c$ is uniquely determined even when no universal set is specified.

If $A=\{p,q\}$, how many subsets does $A$ have?

Let $A_1=\{1,2\}$, $A_2=\{2,3,4\}$, and $A_3=\{4,5\}$. Enter $\bigcup_{i=1}^{3}A_i$ in roster notation.

Let $A=\{1,2\}$ and $B=\{x,y\}$. Which ordered pair belongs to $A\times B$?

Let $A=\{1,2,3,4\}$ and $B=\{2,4\}$. Which set equals $A\setminus B$?

Let $A=\{1,2,3,4\}$ and $B=\{3,4,5,6\}$. Which set is $A\cup B$?

Let $A=\{2,4\}$ and $B=\{2,4,6\}$. Which relationship between $A$ and $B$ is correct?

Given $U=\{1,2,3,4,5,6\}$ and $A=\{1,4\}$, which set is the complement $A^c$ relative to $U$?

If $A=\{p,q,r\}$, how many elements does the power set $\mathcal{P}(A)$ have?

True or false: If $A\cap B=\varnothing$, then $A$ and $B$ are disjoint.

Let $A_1=\{1,2\}$, $A_2=\{2,3,4\}$, and $A_3=\{4,5\}$. What is the cardinality of $\bigcup_{i=1}^{3}A_i$?

Let $A=\{1,2,3,4\}$ and $B=\{2,4,6\}$. What is the cardinality of $A\setminus B$?

Use element chasing to prove the set identity

Show the membership equivalences that establish the result.