Question

For which operations is the set {–1, 1} closed?



Choose all answers that are correct.


A.
addition


B.
subtraction


C.
multiplication


D.
division

Answer 1

HEEEELLPPPPP

Answer 2

Do you know what it means for an operation to be closed on a set?

Answer 3

yes

Answer 4

i know Natural numbers: {1, 2, 3 ,…}
Whole numbers: {0, 1, 2, 3,…}
Integers: {…, –3, –2, –1, 0, 1, 2, 3,… }
Rational numbers: numbers that can be written as a fraction. This includes terminating or repeating decimals.

Answer 5

anyone help

Answer 6

Well this question only pertains to the set \( A = \{ -1, 1 \}\). We then pair the set with an operation, like addition so \((A, +) \). This structure will be closed if for any elements \( a, b \) in \( A \) we get another element in \(A\).

So for \( (A, +) \) the only combinations we have are:
\(1 +1 \), \(-1+1\), \(-1+-1\). If any of these DONT return either \(1\) or \(-1\) then the set is not closed under addition. All of them return other elements, so \(A\) is not closed under addition.

Using this definition, you should be able to check the other operations.

Answer 7

so its a b d

Answer 8

Well a is addition and was just shown to not be closed, so it cannot be a. In the same manner, subtraction of \( \{-1,1\} \) produces numbers outside of the set, so that is open. Multiplication and division however, may not, since 1 is the multiplicative identity.

Answer 9

@TayTay23

Answer 10

so its multipataion and division

Answer 11

its mutlipul choice there more than one answer

Answer 12

Correct since \(-1 \times 1 = -1 \), \(-1 \times -1 = 1 \), and \( 1 \times 1 = 1\) then A is closed under multiplication. The same holds for division.

The question states there may me multiple correct answers

Answer 13

yes