Is Q a subset of Z?

Question

Need to explain why true or false

Answer 1

N is the set of natural numbers. Like {1, 2, 3, ....}

Z is the set of integers. This can be negative or positive. {..., -3, -2, -1, 0, 1, 2, 3,...}

As you can see N is a subset of Z.

 

Now what is Q? Q is the set of rational numbers. A rational number can be written p/q where p can be an integer and q can be a natural number (This prevents dividing by 0).

Examples 1/2, -2/3, 3/4,... are rational numbers. Also note 1, -3 are rational numbers because we can write 1 = 1/1 and -3 = -3/1.

From this you see Z is a subset of Q.

 

We then have the set of irrational numbers which are numbers that cannot be written as p/q. Examples include pi, e, square root of 2, ....

 

With these we can define the set of Real numbers, R which contains rational and irrational numbers

 

So from all this you see N is a subset of Z which is a subset of Q which is a subset of R.

 

Hope that is helpful.

Thanks - David