Seven is part of all of the following sets of numbers except O irrational numbers
O integers
O rational numbers
natural numbers

Seven isn't part of the set of irrational numbers.

Step-by-step explanation:

Start with the smallest set among the choices. The set of all natural numbers, , starts with (or , for some people.) A number is in (write ) if and only if is in . Conversely, if is indeed in , then would also be in . For :

.

.

.

Therefore, is indeed in the set of all natural numbers.

Similarly, a number is in the set of integers, , if and only if either or is (or both are) in .

Conversely, if a number is in , then both and will be in .

It can be shown in a similar iterative way that .

Alternatively, consider the fact that the set of all natural numbers, , is a subset of the set of all integers, . Therefore, implies that .

A number is a member of the set of all rational numbers if and only if there exists two integers and such that:

.

and are both integers. If and , then . Hence,

Alternatively, note that the set of all integers, , is a subset of the set of all rational numbers, . Therefore, the fact that would imply that .

A number is in the set of all irrational numbers if and only if:

Therefore, the fact that is a rational number implies that it is not an irrational number.

irrational numbers

Step-by-step explanation:

d. all of the above

step-by-step explanation: