Set Notation & Venn Diagrams Flashcards

All 9 cards in this deck

What does $A \cap B$ mean?

The intersection: the elements that are in both $A$ and $B$ — the overlap of the two circles.

True or false? $A \cup B$ means the elements that are in both $A$ and $B$.

False. That is $A \cap B$; the union $A \cup B$ is everything in $A$, in $B$, or in both.

What does $A'$ mean?

The complement of $A$: all the elements of the universal set that are not in $A$.

In a Venn diagram, what does $\xi$ (also written $E$) stand for?

The universal set: all the elements being considered, shown by the rectangle around the circles.

A number is chosen at random from the universal set $\xi$. How do you find $P(A \cup B)$ from a completed Venn diagram?

Count the elements in every region inside either circle and divide by the total number of elements in $\xi$.

e.g. $5$ elements in $A \cup B$ out of $9$ gives $\frac{5}{9}$.

What are the steps to complete a two-set Venn diagram from given frequencies?

e.g. $30$ people: $18$ like tea, $12$ like coffee, $7$ like both

1. Write the intersection first: $7$ in tea $\cap$ coffee.
2. Subtract it from each set total: tea only $18-7=11$, coffee only $12-7=5$.
3. Subtract all three regions from the universal total for outside: $30-(11+7+5)=7$.

True or false? If $18$ people like tea and $7$ like both tea and coffee, you write $18$ in the 'tea only' region of the Venn diagram.

False. $18$ is the total for the whole tea circle; 'tea only' is $18-7=11$.

Which region of a three-set Venn diagram should you fill in first, and why?

The middle, $A \cap B \cap C$ — every other overlap includes it, so it must be subtracted out of them.

What are the steps to complete a three-set Venn diagram from overlap totals?

e.g. $30$ people; $4$ do all three; $10$ do $A$ and $B$; $7$ do $B$ and $C$; $6$ do $A$ and $C$; $15$ do $A$; $18$ do $B$; $13$ do $C$

1. Put the 'all three' number in the middle: $4$.
2. Pair region $=$ pair total $-$ middle: $A\cap B$ only $=6$, $B\cap C$ only $=3$, $A\cap C$ only $=2$.
3. 'Only' region $=$ set total $-$ its other regions: $A$ only $=3$, $B$ only $=5$, $C$ only $=4$; outside $=30-27=3$.