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3 years ago

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.

Mathematics

2 answers:

ankoles [38]3 years ago

4 0

Answer:

Step-by-step explanation:

To prove: The sum of a rational number and an irrational number is an irrational number.

Proof: Assume that a + b = x and that x is rational.

Then b = x – a = x + (–a).

Now, x + (–a) is rational because addition of two rational numbers is rational (Additivity property).

However, it was stated that b is an irrational number. This is a contradiction.

Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.

Hence, the sum of a rational number and an irrational number is irrational.

Goryan [66]3 years ago

4 0

Answer:

I believe the answer is B

Step-by-step explanation:

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See image for question.

kotegsom [21]

Answer:

(a)

<u>Sample space:</u>

1*1, 1*2, 1*3, 1*4,
2*1, 2*2, 2*3, 2*4,
3*1, 3*2, 3*3, 3*4,
4*1, 4*2, 4*3, 4*4

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(b)

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(a) <u>Sample space:</u>

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