Which operations is the following set closed under: {... , -3, -1, 1, 3, ...}?

2 answers:

6 0

I'd say it's closed for multiplication and division.
Any member of the set, when multiplied or divided by
any other one, produces another member of the set.

Ganezh [65]3 years ago

5 0

Not addition, since $-1+1=0$ and 0 doesn't belong to the set.

Not subtraction, since $1-1=0$ .

It is closed under multiplication. The set appears to contain all non-zero multiples of 3.

Not division, since dividing some of the numbers results in rationals which do not belong to the set.

What other operations are you supposed to consider?

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Do line segments with the given lengths form a right triangle? State whether the line segments with the given lengths form a rig

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Given:

19, 180, 181

To be able to determine if the given lengths form a right triangle, the following condition must be met:

$\text{ a}^2\text{ + }b^2=c^2$

Let's check.

a.) At a = 19, b = 180, c = 181

$\begin{gathered} \text{ a}^2\text{ + }b^2=c^2 \\ (19)^2+(180)^2=(181)^2 \\ 361\text{ + 32,400 = 32,761} \\ 32,761\text{ = 32,761} \end{gathered}$

Therefore, the given lengths could form a right triangle at a = 19, b = 180 and c = 181.

The answer is yes.

It just happened to be that we got the right answer on the first try, you must also examine at a = 180, b = 181, c = 19 and a = 181, b = 19, c = 180 if the first try didn't meet the right condition.

If you failed to get, then the given lengths could not form a right triangle. The answer would be no.

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