6.3cFoundation tier4MA1 · Section 6: Statistics and probability

Set notation and Venn diagrams

Key learnings

Know the symbols
$A\cap B$ = in both (intersection); $A\cup B$ = in either (union); $A'$ = not in $A$ (complement); $\xi$ = the universal set; $\varnothing$ = the empty set; $n(A)$ = the number of elements in $A$ .
Fill the overlap first
Always put the "both" (intersection) value in the centre first, then subtract to get the "only" regions; remember the region outside the circles.
Union formula
$n(A\cup B) = n(A) + n(B) - n(A\cap B)$ — subtract the overlap so it is not counted twice.

Drawn from real examiner reports.

n(...) means the NUMBER of elements, not the elements

Listing the elements (e.g. {4,7}) when $n(\ldots)$ asks for how many there are.

Not subtracting the overlap from a circle total

Writing the full set total in the "only" region instead of subtracting those who are in both.

Forgetting the region outside the circles

Omitting the elements in the universal set that are in neither $A$ nor $B$ .

Guessing instead of shading the required region

On set-notation questions, not shading the region asked for and so picking the wrong parts.

Shade the region the notation describes
Before reading values, shade exactly what the notation means — it stops you combining the wrong regions.

Symbol	Meaning
$A\cap B$	intersection — in both $A$ and $B$
$A\cup B$	union — in $A$ or $B$ (or both)
$A'$	complement — not in $A$
$\xi$	the universal set (everything)
$\varnothing$	the empty set (no elements)
$n(A)$	the number of elements in $A$

Note that $n(A)$ is a count, not a list of the elements.

Foundation

What does A ∩ B mean?

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Question 1 of 1Foundation3 marks

In a group of $30$ students, $18$ study French, $14$ study German and $5$ study both. How many study (a) French only, (b) neither subject?

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