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}?

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}

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

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:

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

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:

Learn more about complement set here:

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