Question

Let P be the set of integers that are multiples of 3 between 1 and 20 and Q be the set of even natural numbers up to 15. Which of the following sets is NOT a subset of the union of P and Q ?Select the correct answer below:{3,5,6,12}{6,12}[3,6,12]{3,6,12,15}

Answer 1

Answer: {3,5,6,12}

Explanation:

Since P={3,6,9,12,15,18} and Q={2,4,6,8,10,12,14}, then the set P∪Q={2,3,4,6,8,9,10,12,14,15,18} consists of every even integer less than 15 in addition to every multiple of 3 that is less than 20. The number 5 is neither even nor a multiple of 3, so it cannot belong to the set P∪Q. Since it is an element of the set {3,5,6,12}, this set is not a subset of P∪Q. The other three choices all consist entirely of elements within P∪Q, so they are subsets of P∪Q.

Answer 2

Given:

• P is the set of integers that are multiples of 3 between 1 and 20.

,

• Q is the set of even natural numbers up to 15.

The elements of P and Q are:

`\begin{gathered} P=\{3,6,9,12,15,18\} \\ Q=\{2,4,6,8,10,12,14\} \end{gathered}`

The union of P and Q is:

`P\cup Q=\{2,3,4,6,8,9,10,12,14,15,18\}`

We observe that 5 is not in the union of P and Q, therefore, the set that is NOT a subset of the union of P and Q is:

{3,5,6,12}

The correct choice is A.