Question

Given A = {3,4, 13, 15) and B = { 13, 15, 21, 25, 30, 37). Which of the following are true? I. AUB 13,4,21,25, 30, 37) III. ACB II. AnB-(13, 15) a) I and III only b) OII only e) Oll and III only d) I and II only e) OI, II, and III None of the above

Answer 1

The correct statements regarding the sets A and B is:

II.

`A\bigcap B=\{13,15\}`

Explanation:

We are given set A as:

`A=\{3,4,13,15\}`

and set B as:

`B=\{13,15,21,25,30,37\}`

and the three statements are given by:

I.

`A\bigcup B=\{12,4,21,25,30,37\}`

II.

`A\bigcap B=\{13,15\}`

III.

`A\subset B`

• We know that the union of two sets is the collection of all the elements which belong either to A or to B.

i.e. from the given sets we have:

`A\bigcup B=\{3,4,13,15,21,25,30,37\}`

• Also, the intersection of two sets is the collection of all the elements which belongs to both the set.

i.e.

`A\bigcap B=\{13,15\}`

• Also, we know that A is a subset of B if:

All the elements of A are contained in B.

But from the given sets we see that:

3,4 belongs to A but they do not belong to B.

Hence, A is not a subset of B.