Logic problem: True or False? If n^2 = 4, then n=-2.

[Shmuel]

True or False?

If n^2 = 4, then n=-2.

I understand that n can = 2 or -2, so do I interpret the '=' sign as "CAN equal" or "MUST equal(only)". meaning, can there be more than one answer to a logic problem and still be true?

 

[ksdhart2]

True or False?

If n^2 = 4, then n=-2.

I understand that n can = 2 or -2, so do I interpret the '=' sign as "CAN equal" or "MUST equal(only)". meaning, can there be more than one answer to a logic problem and still be true?

I tend to think of the equality operator as saying that (something) equals (something else), and only (something else). Operating under that logic, the statement "If n² = 4, then n=-2." is false. In the "language" of math, "true" means "always true, in all cases", whereas "false" may mean "always false" or "sometimes true."

If I were to write out the solutions to n² = 4, there are three ways I might use. I could write \(\displaystyle n = \pm 2\) or \(\displaystyle n=2 \text{ or } n=-2\), or \(\displaystyle n\in \left\{2,-2\right\}\).

 

[Deleted member 4993]

I tend to think of the equality operator as saying that (something) equals (something else), and only (something else). Operating under that logic, the statement "If n² = 4, then n=-2." is false. In the "language" of math, "true" means "always true, in all cases", whereas "false" may mean "always false" or "sometimes true."

If I were to write out the solutions to n² = 4, there are three ways I might use. I could write \(\displaystyle n = \pm 2\) or \(\displaystyle n=2 \text{ or } n=-2\), or \(\displaystyle n\in \left\{2,-2\right\}\).

I would add one more way: |n| = 2

 

[Harry_the_cat]

True or False?

If n^2 = 4, then n=-2.

I understand that n can = 2 or -2, so do I interpret the '=' sign as "CAN equal" or "MUST equal(only)". meaning, can there be more than one answer to a logic problem and still be true?

"If n=-2, then n^2 =4" is definitely a TRUE statement.

"If n^2=4, then n=-2" is not necessarily a true statement ... it may be true, but then again it may be false.

An analogy:

"If it rains tomorrow, I will take my umbrella" - TRUE

compared to

"If I take my umbrella tomorrow, it will rain"- not necessarily true.

 

[Otis]

If n^2 = 4 then n = -2

n is a variable; it takes on many values, one at a time

Case n=-2: the statement above is true

Case n=2: the statement above is false