Question

Luke says you can always add and multiply to join groups is he correct explain why or why not

Answer 1

Forming groups , when you Add and multiply numbers is always True.

Because when you Add and Multiply two numbers in the same set, you get elements belonging to same set.

But this is not Possible in case of Division and Subtraction always.

For example

In case of Natural number

2-3= -1, is not a natural number.

And ,when you divide 2 by 3,
`=(2)/(3)`, the output will not be a natural number.

So, Subtraction and Division will not always form group.

Apart from ,these two operation, Addition,and , Multiplication , there are Other Operations which can be used for forming groups , like HCF and LCM , in this also we use two basic operation Multiplication and Addition to form groups.

Yes, Luke is true that, you can always add and multiply to join groups.

Answer 2

Well if you divide or subtract groups, you'll end up with a smaller number. You won't be joining groups, but dividing them/subtracting them.