3 years ago

Please help me on problems 17,18,19,20...explanation needed Thanks:)

Mathematics

1 answer:

nordsb [41]3 years ago

5 0

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morpeh [17]

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Novay_Z [31]

The first one is rectangle

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Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.

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Proof by contadiction.

Let assume there exist such positive integers $a$ and $b$ whose sum is a prime number $p$ , that their greatest common divisor is greater than 1.

$a,b\in\mathbb{Z^+}\\d=\text{gcd}(a,b)>1\\\\a=de\\b=df\\e,f\in\mathbb{Z^+}\\\\a+b=p\\de+df=p\\d(e+f)=p\\$

Since $p$ is a prime number and $d>1$ , then $d=p \wedge e+f=1$ , but we assumed earlier that $e,f\in\mathbb{Z^+}$ , and there are no two positive integers that sum up to 1.

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3 years ago

Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion.

jeyben [28]

<span>The hypothesis is : If Robbie wants to save money to buy a car. Conclusion : he must get a part-time job.

Robbie already started the new job yesteday. So, that makes the hypothesis true.

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Zina [86]

The first answer is correct because the terms are alike in both expressions

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