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Pani-rosa [81]
3 years ago
14

Which axiom is used to prove that the product of two rational numbers is rational

Mathematics
1 answer:
aliina [53]3 years ago
5 0

Answer:

First, a rational number is defined as the quotient between two integer numbers, such that:

N = a/b

where a and b are integers.

Now, the axiom that we need to use is:

"The integers are closed under the multiplication".

this says that if we have two integers, x and y, their product is also an integer:

if x, y ∈ Z ⇒ x*y ∈ Z

So, if now we have two rational numbers:

a/b and c/d

where a, b, c, and d ∈ Z

then the product of those two can be written as:

(a/b)*(c/d) = (a*c)/(b*d)

And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:

(a*c)/(b*d)

is the quotient between two integers, then this is a rational number.

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Solve the equation cot 2x + cot x =3
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7. In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment th
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b) P(7 of the players number are drrawn)=3.33×10^-c) P(at least 6 of the players number were drawn)=1.84×10^-4

Step-by-step explanation:

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There are approximately 5400chances that at least6 of the numbers drawn are chosen by the player.

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