Question

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?


Which set is an empty set?


Which set would contain the subset E = {1, 3, 5, 7}?

Answer 1

- Complement of B (with universe U = all integers): D (the odd integers).
- The empty set: C, because 2x is always even for integer x, so no integer makes 2x odd.
- The set that contains E = {1,3,5,7}: D (the odd integers).