Question

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

The universal set contains all possible elements in the set

• The complement of set B is the set D.
• The empty set is the set C
• The set D contains the subset E = {1, 3, 5, 7}

The complement of set B

The sets are given as:

• 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}

Where the universal set is:

U = {all integers}

The set B is the set of all even integers.

So, its complement would be the set of all odd integers i.e. set D

Hence, the complement of set B is the set D.

The empty set

From the set definition, we have:

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

This means that the set C contains elements 2x, where 2x is an odd number.

The element x is an integer, and twice an integer (i.e. 2x) is an even number.

This means that 2x cannot be an odd number;

Hence, the empty set is the set C;

The set that contains the subset E = {1, 3, 5, 7}

The subset E = {1, 3, 5, 7} contains odd integers.

From the set definition, set D represents the set of odd integers

Hence, the set D contains the subset E = {1, 3, 5, 7}

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