Question

a.) Assume the universal set is U = {1, 2, 3, 4, 5, 6}, like when rolling a single six-sided die.

Write two sets where the intersection is empty and the union is the universe.

b.) True or False: For any set A,

True or False: For any set A,

Answer 1

Assume the universal set is U = {1, 2, 3, 4, 5, 6}, like when rolling a single six-sided die.

Let Event A: even number appears. The possible outcomes are:

A={2,4,6}

Let Event B : Odd number appears. The possible outcomes are:

B={1,3,5}

The intersection of A and B is the common elements in two events A and B is given by:

A B ={ } =

There is no common element between A and B therefore the intersection is empty set.

The A union B is the elements in A, in B or in A and B. It is represented as A B and is given by:

A B ={1, 2, 3, 4, 5, 6} = U

Which is the universe U. Therefore the union of two sets A and B is Universe.

b) For any set of A , maybe be it's not true.

e.g.Let ,A=The number is less than 4 appear

A={1, 2, 3}

Let Event B : Odd number appears. The possible outcomes is:

B={1,3,5}

A B ={1,3}

A B ={1,2,3,5}

Here it not true the intersection is empty and the union is the universe.