Question

1 fill in the blank 5 points
how many sides on a 6 - sided die are even? type your answer...
how many sides on a 6 - sided die are divisible by 3? type your answer...
how many sides on a 6 - sided die are even and divisible by 3? type your answer...
according to the idea behind the union rule (and the three previous parts), how many sides on a 6 - sided die are even or divisible by 3? type your answer...
which set represents the union of the even numbered rolls of a die with the rolls divisible by 3? choose your answer...

Explanation:

Step1: List even - numbered sides

The sides of a 6 - sided die are 1, 2, 3, 4, 5, 6. The even - numbered sides are 2, 4, 6. So there are 3 even - numbered sides.

Step2: List sides divisible by 3

The sides divisible by 3 on a 6 - sided die are 3, 6. So there are 2 sides divisible by 3.

Step3: Find sides that are even and divisible by 3

The number that is both even and divisible by 3 among 1 - 6 is 6. So there is 1 side that is even and divisible by 3.

Step4: Use the union rule

The union rule for two sets \(A\) and \(B\) is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, \(n(A) = 3\) (even - numbered sides), \(n(B)=2\) (sides divisible by 3), and \(n(A\cap B) = 1\). So \(n(A\cup B)=3 + 2-1=4\).

Step5: Determine the union set

The set of even - numbered rolls is \(\{2,4,6\}\), and the set of rolls divisible by 3 is \(\{3,6\}\). The union of these two sets is \(\{2,3,4,6\}\).

Answer:

3
2
1
4
{2,3,4,6}