Question

Consider the statement that the product of two of the numbers 651000 − 82001 + 3177, 791212 − 92399 + 22001, and 244493 − 58192 + 71777 is nonnegative (for the purpose of this agreement, we will think of 0 as carrying a positive sign).Identify the correct proof of the given statement.(You must provide an answer before moving to the next part.)NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the statement that the product of two of the numbers 651000 - 82001 - 3177791212-92399 22001, and 244493_58192+71777 is nonnegative (for the purpose of this agreement, we will think of O as carrying a positive sign). Identify the correct proof of the given statement. (You must provide an answer before moving to the next part.) A) Of these three numbers, at least two numbers must be negative, since there are only two signs. The product of these two numbers is nonnegative. B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative. C) Of these three numbers, all three must have the same sign. Thus, the product of any two numbers is nonnegative. D) Of these three numbers, at least two must have the same sign, since there are only two signs. The product of two with the same sign is nonnegative. E) Of these three numbers, at least two must have the same sign. The product of one of these numbers and the third number is nonnegative.

Answer 1

Answer:

a c

Step-by-step explanation:

Answer 2

Non-negative numbers are numbers that are either positive or zero.

The correct statement of this proof is (c) Of these three numbers, all three must have the same sign. Thus, the product of any two numbers is non-negative.

Let the numbers be a, b and c.

Such that:

$a = 65^{1000} - 8^{2001} + 3^{177}$

$b =79^{1212} - 9^{2399} + 2^{2001}$

$c = 24^{4493} - 5^{8192} + 7^{1777$

For the product of any two numbers to be non-negative, it means that both numbers have the same sign (i.e. both negative or both non-negative)

Assume all numbers are non-negative $\{+a, +b, +c\}$

The product of any two numbers will be non-negative

$+a \times + b =+ab\\+a \times + c=+ac\\+b \times + c =+bc$

Assume all numbers are negative $\{-a, -b, -c\}$

The product of any two numbers will also be non-negative

$-a \times - b =+ab\\-a \times - c=+ac\\-b \times - c =+bc$

Hence, the correct statement of this proof is (c) all numbers must have the same sign

Read more about negative and non-negative numbers at:

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