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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}?

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ashiramorris77owi9v2

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?
D
 Which set is an empty set?
C 
Which set would contain the subset E = {1, 3, 5, 7}?
D

You can use the definition of complement of a set to find the complement of set B.

  • The complement set to B is B' = D
  • The set C is an empty set.
  • The set which contains E = {1. 3. 5. 7} is D

What is a complement of a set?


Firstly there is a universal set in which all the remaining sets in the given context lies. Now, let the target set be B whose complement set has to be found. Let the universal set be U, then we have the complement set of B as:

B' = U - B (remove all elements from the set U which lies in set B)

or it is written as:

[tex]B' = \{ x \in U | x \notin B\}[/tex]

Thus, we can write the complement set of B in two ways:

[tex]B' = \{ x \in U | x \notin B\}[/tex]

or

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

B'  =  {x | x ∈ U and x is an odd integer}  = D (since if an integer is not even, then it must be odd)

The set C is empty since 2x for an integer x is always even (considering the given fact that 0 is to be assumed even too). Since no 2x is going to be odd, thus, C is an empty set.

Since set A contains all integer > 3, and set B contains even integers and set C is empty, and since set D contains all odd integers, thus the set D contains the given set E = {1, 3, 5, 7}

Thus, we have:

  • The complement set to B is B' = D
  • The set C is an empty set.
  • The set which contains E = {1. 3. 5. 7} is D

Learn more about complement set here:

https://brainly.com/question/24403298

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