Union of Sets

Question 1

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

Accepted Answer

$\{1,2,3,4,5\}$ — Combine all elements, listing the shared $3$ once: $\{1,2,3,4,5\}$.

Question 2

The symbol $\cup$ represents:

Accepted Answer

Union — $\cup$ is the union symbol.

Question 3

$A \cup B$ is the set of elements in:

Accepted Answer

$A$ or $B$ (or both) — Union collects every element in either set.

Question 4

If $n(A)=10$, $n(B)=7$ and $n(A\cap B)=4$, then $n(A\cup B) =$

Accepted Answer

13 — $n(A\cup B)=n(A)+n(B)-n(A\cap B)=10+7-4=13$.

Question 5

If $A=\{a,b\}$ and $B=\{c,d\}$, then $n(A\cup B) =$

Accepted Answer

4 — The sets are disjoint, so $n(A\cup B)=2+2=4$.

Question 6

For any set $A$, $A \cup A =$

Accepted Answer

$A$ — Combining $A$ with itself adds nothing new, so $A\cup A = A$.

Question 7

For any set $A$, $A \cup \varnothing =$

Accepted Answer

$A$ — The empty set adds no elements, so $A\cup\varnothing = A$.

Question 8

If $A \subset B$, then $A \cup B =$

Accepted Answer

$B$ — Since all of $A$ is already inside $B$, the union is $B$.

Question 9

If $A=\{2,4,6,8\}$ and $B=\{4,8,12\}$, then $A\cup B =$

Accepted Answer

$\{2,4,6,8,12\}$ — Combine all, listing repeats once: $\{2,4,6,8,12\}$.

Question 10

In a group, $15$ like tea, $20$ like coffee and $5$ like both. How many like tea or coffee?

Accepted Answer

30 — $n(	ext{tea}\cup	ext{coffee})=15+20-5=30$.