Question

Let U = {all integers}. Consider the following sets: 3 questions. Choose A, B, C, or D for each? (Sets and Venn Diagrams lesson)

Let U = {all integers}.

Consider the following sets:

A = {x | x ∈ U and x > 3}

B = {x | x ∈ U and x is an even integer}

C = {x | x ∈ U and 2x is an odd integer}

D = {x | x ∈ U and x is an odd integer}

Use the defined sets to answer the questions.

Assuming 0 is an even integer, which set is the complement to set B?
A, B, C, or D
Which set is an empty set?
A, B, C, or D
Which set would contain the subset E = {1, 3, 5, 7}?
A, B, C, or D

Answer 1

See below.

Explanation:

Question 1.

The complement of set `B` written `B'` is the set of everything in `U` that is not in `B`. If `U` is all the integers and `B` is all the even integers, then `B'` is all the odd integers. `D`.

`B'=D`

Question 2.

The empty set written `cancel(O)` is the set containing no elements. Set `C` is 2 times an odd integer, which is always an even number, so it can't be an odd number. Therefore:

`C=cancel(O)`

Question 3.

A subset is a set that contains elements that belong to another set. Set `E` contains the first four odd integers, therefore it is a subset of the set of all odd integers `D`

This is written:

`EsubD`