Question

A is the set of even numbers greater than or equal to 4 and less than or equal to 8B=1-29, -25,-24, -22, -21, 22, 27(a) Find the cardinalities of A and B.n(A)=3(b) Select true or false.12 € A22 € B67 A-24 € BTruen(B) = 1FalseX%S3

Answer 1

Step-by-step explanation

Set A is composed of all the even numbers equal or greater than 4 and equal or less than 8 so set A is:

`A=\lbrace4,6,8\rbrace`

The cardinalities of A and B are equal to their number of elements so we have n(A)=3 and n(B)=7.

With both sets explicitly written we can complete the true or false table. The only thing to take into account is that the symbol ∈ means "belongs to" and that ∉ means "does not belong to".

The first statement of the table is:

`12\in A`

This is false because 12 does not belong to set A since it is not included in it.

The second statement is:

`22\in B`

As you can see 22 is in deed one of the elements of set B which means that this statement is true.

The third one is:

`6\\otin A`

This statement is false because as we saw before 6 is an element of set A.

The last statement is:

`-24\in B`

As you can see -24 is one of the elements of set B so this statement is true.

Answers

False

True

False

True