Question

Are the following statements equivalent:

Answer 1

Answer:

all statements discuss the multiplication of two numbers (we can say they are equivalent based on this context)

first three statements are exactly the same

last three statements are exactly the same

Explanation:

Let's go through the statements one by one:

1) ab > 0 and “a>0, b>0”

We know that when multiplying two positive numbers, the result is always a positive number.

Examples:

2 * 3 = 6

$\frac{1}{4} * \frac{2}{5} = \frac{2}{20} = \frac{1}{10}$

We can note that when the two operands are positive, the result is also positive

2) ab > 0 and “the numbers a and b are of the same sign”

We know that when multiplying two positive numbers or two negative numbers, the result will always be positive

Examples:

2 * 3 = 6

-2 * -3 = 6

We can note that when the two operands have the same sign, the result is positive

3) ab > 0 and “a>0, b>0 or a<0, b<0”

This choice is actually the same as the previous one.

When the two numbers are positive: a > 0 and b > 0

Wen the two numbers are negative: a < 0 and b < 0

Therefore, it is just a paraphrasing of statement 2

4) ab < 0 and “a>0, b<0”

We know that when we multiply numbers of different signs, the result will always be negative

Examples:

2 * -3 = -6

$\frac{-1}{4} * \frac{2}{5} = \frac{-2}{20} = \frac{-1}{10}$

We can note that when the two operands have different signs, the result is negative

5) ab < 0 and “a<0, b>0 or a>0, b<0”

This is the same as statement 4 as it shows that the two operands have different signs (one is greater than zero while the other is less than zero), their product will be a negative number (less than zero)

6) ab < 0 and “the numbers a and b are of different signs”

This is the same as statement 5. It is only a paraphrase of the words.

Based on the above, we can conclude that:

1- all statements discuss the multiplication of two numbers

2- first three statements are exactly the same

3- last three statements are exactly the same

Hope this helps :)