Pancyprian Examinations (Cyprus) · Mathematics

Sets and inclusion-exclusion

6 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 6 questions

In a class of $40$ students, $25$ study French, $18$ study Spanish and $8$ study both. How many study neither language?
For finite sets, $∣ A ∣ = 30$ , $∣ B ∣ = 22$ and $∣ A \cup B ∣ = 45$ . What is $∣ A \cap B ∣$ ?
Out of $100$ people, $60$ drink tea, $50$ drink coffee and $20$ drink neither. How many drink both?
In a survey $∣ A ∣ = 20$ , $∣ B ∣ = 15$ , $∣ C ∣ = 12$ , $∣ A \cap B ∣ = 6$ , $∣ A \cap C ∣ = 5$ , $∣ B \cap C ∣ = 4$ and $∣ A \cap B \cap C ∣ = 2$ . What is $∣ A \cup B \cup C ∣$ ?
Which set is equal to $(A \cup B)^{'}$ , the complement of $A \cup B$ ?
A set has $5$ elements. How many of its subsets contain one particular element?

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