Flashcards · 10 cards

Sets & Venn diagrams

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Rule
What does $B \subseteq A$ mean?
Answer
Every element of $B$ is also in $A$ : $B$ sits inside $A$ .
B ⊆ AB sits inside A: every element of B is in A
From the lesson: Sets and set notation
Rule
What is $A \cup B$ ?
Answer
The union: everything in $A$ or $B$ or both.
A ∪ BUnion: in A or B or both
From the lesson: Sets and set notation
Rule
What is $A \cap B$ ?
Answer
The intersection: only what is in both $A$ and $B$ .
A ∩ BIntersection: in both A and B
From the lesson: Sets and set notation
Rule
What is $A'$ ?
Answer
The complement: everything in $U$ that is not in $A$ . Write $U$ out first, then cross off the elements of $A$ .
A'Complement: in U but not in A
From the lesson: Sets and set notation
Rule
What are disjoint sets?
Answer
Sets with nothing in common: $A \cap B = \varnothing$ .
Disjoint setsNo overlap: A ∩ B = ∅
From the lesson: Sets and set notation
Know it
$(A \cup B)' = \,?$
Answer
$A' \cap B'$ . And $(A \cap B)' = A' \cup B'$ .
From the lesson: Sets and set notation
Know it
How many whole numbers are there between 5 and 12?
Answer
6: they are 6, 7, 8, 9, 10 and 11. "Between" leaves out both ends.
From the lesson: Sets and set notation
Rule
$n(A \cup B) = \,?$
Answer
$n(A) + n(B) - n(A \cap B)$ : adding $n(A)$ and $n(B)$ counts the overlap twice.
n(A ∪ B)n(A) + n(B) counts 'both' twice, so subtract it once
From the lesson: Venn diagram problems
Know it
Filling a Venn diagram from counts: where do you start?
Answer
In the middle (the overlap), then work outwards. "28 like rice" includes those who like both, so rice only is 28 minus the overlap.
From the lesson: Venn diagram problems
Which method?
WAEC 2021 · Paper 2 · Q6 (a)
In a class of 80 students, $\frac34$ study Biology and $\frac35$ study Physics. If each student studies at least one of the subjects: (i) draw a Venn diagram to represent this information; (ii) how many students study both subjects? (iii) find the fraction of the class that study Biology but not Physics.
How do you find how many study both?
Answer
Let $x$ study both. Then Biology only is $60 - x$ and Physics only is $48 - x$ . Nobody is outside, so the three regions add up to 80.
From the lesson: Venn diagram problems Try the question