Intersection of Sets

Question 1

If $A=\{1,2,3,4\}$ and $B=\{3,4,5,6\}$, then $A \cap B =$

Accepted Answer

$\{3,4\}$ — The common elements of both sets are $3$ and $4$, so $A\cap B=\{3,4\}$.

Question 2

The symbol $\cap$ represents:

Accepted Answer

Intersection — $\cap$ is the intersection symbol.

Question 3

If $A=\{a,b,c\}$ and $B=\{d,e\}$, then $A \cap B =$

Accepted Answer

$\varnothing$ — The sets share no elements, so their intersection is the empty set $\varnothing$.

Question 4

$A \cap B$ is the set of elements that are in:

Accepted Answer

Both $A$ and $B$ — Intersection collects elements belonging to both sets.

Question 5

If $n(A)=8$, $n(B)=6$ and $n(A\cap B)=3$, how many elements are in $A$ only?

Accepted Answer

5 — $A$ only $= n(A)-n(A\cap B)=8-3=5$.

Question 6

If $A=\{	ext{factors of }12\}$ and $B=\{	ext{factors of }18\}$, then $A\cap B =$

Accepted Answer

$\{1,2,3,6\}$ — Factors of $12$: $1,2,3,4,6,12$; factors of $18$: $1,2,3,6,9,18$. Common: $\{1,2,3,6\}$.

Question 7

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

Accepted Answer

$A$ — Every element of $A$ is in $A$, so $A\cap A = A$.

Question 8

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

Accepted Answer

$\varnothing$ — The empty set shares no elements with $A$, so $A\cap\varnothing=\varnothing$.

Question 9

If $A \subset B$ ($A$ is a subset of $B$), then $A \cap B =$

Accepted Answer

$A$ — Since every element of $A$ is already in $B$, the common part is $A$ itself.

Question 10

In a class of $30$, $18$ play football and $12$ play chess; $7$ play both. Then $n(	ext{football}\cap	ext{chess})=$

Accepted Answer

7 — The number playing both is exactly the intersection, so $n(	ext{football}\cap	ext{chess})=7$.