Question

Which of the following gives an example of a set that is closed under multiplication? Choose all that apply.



The product of an even number and an even number


The product of an odd number and an odd number


The product of a negative number and a negative number


The product of a perfect cube and a perfect cube

Answer 1

If a set is closed under a binary operation like multiplication, it means that the product of any two elements in the set is also in the set.

Answer 2

1) Is the product of two even numbers even?

Answer 3

Even Number =2k
odd Number is =2K+1

Product of 2 even number : \((2k)*(2m)=4km=2(2km) \)
Product of 2 odd numbers: \((2k+1)(2m+1)=4km+2k+2m+1=2(2km+k+m)+1\)
Product of two negative numbers: \(-k*-m=km\)
Product of 2 perfect cubes=\(k^3*m^3=(km)^3\)

Answer 4

Thank you !!!!!

Answer 5

Do you understand the solution?

Answer 6

yes i do now

Answer 7

Hola

Answer 8

For even and odd there is an easier way of thinking about it. An even number must contain a power of the prime factor \(2\) odd numbers cannot contain the prime factor \(2\). So if you consider any two even numbers clearly both numbers contain the prime factor 2 and so the product will. Similarly two odd numbers will both NOT contain the prime factor 2 and so the product will not contain the prime factor 2 and therefore the product is odd.

Answer 9

hola senorita