# P4

QUESTION: Consider a set of numbers: $\{2, 3, 5, 6, 7, 8, 10, 11, 15\}$.Let $A$ be the set of even numbers, and $B$ be the set of prime numbers.

a) Complete the Venn diagram by writing all above numbers in their appropriate sections.

b) State how many values are in $A\cap B$.

c) Find $P(A\cup B)$.

ANSWER: a) Firstly, let’s consider any number that are both even and prime. There is one: 2. This is the only number that will go in the section where the two circles cross over.

Then, the rest of the even numbers: 6, 8, and 10, will go in the section of the A circle that doesn’t cross over with B. Next, the rest of the prime numbers: 3, 5, 7, and 11, will go in the section of the B circle that doesn’t cross over with A.

Finally, the one number that is neither even nor prime is 15, so that goes outside the circles. The completed Venn diagram looks like the one below.

b) $A\cap B$ refers to “$A$ and $B$”. There is only one number in both $A$ and $B$, so the answer is 1.

c) $A\cup B$ refers to “$A$ or $B$”. There are 8 numbers that are contained in circle $A$ and/or circle $B$, and there are 9 numbers in total, so we get

$P(A\cup B)=\dfrac{8}{9}$