Question

show that rational numbers are closed under addition and multiplication​

Answer 1

Answer:

We can prove this by some examples:

1. Taking two rational numbers 2 and -3, we see that 2 + (-3) is commutative as:

• 2 + (-3)
• 2 - 3
• - 1 [It is a rational number.]

2. Taking the same two rational numbers, we see that 2 x -3 is commutative as:

• 2 x - 3
• - 6 [It is a rational number]

This proves that both rational numbers are closed under both addition and multiplication.

Thus,

• a + b gives a unique rational number.
• a x b gives a unique rational number.