Question

Show that the set of rational numbers is a field.

Answer 1

Answer:

Hope this will help you dear friend

Answer 2

Given:

Consider the given set of rational numbers Q

Find:

Need to show that Q is field

Solution:

Since Q is integral domain and without zero divisors therefore It is field.

Integral Domain:

A commutative ring with unity without zero divisors is called Integral domain

If a.b = 0 then a = 0 or b =  0 then ring is said to be without zero divisor

Therefore A commutative ring with unity in which every non-zero element has a multiplicative inverse in the field

Q has multiplicative inverse 1

Q is field.