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I am a dad helping with daughters homework and have a symbol I have not seen, the symbol is a solid diamond. The problem readsCan anyone tell me what I am supposed to do with the solid diamond? Thank you in advance.Quote:
A new operation is defined as a ( solid diamond ) b = a+a-b. Is the set of whole numbers closed under the operation ( solid diamond )? If not, give a set that is closed under this operation.
a (diamond) b=a+a-b
5 (diamond) 2=5+5-2=8
The set of whole numbers is not going to be closed under this new operation (which is simply a combination of familiar operations in addition and subtraction) because the set of whole numbers is not closed under addition and subtraction
Here I am assuming the set of whole numbers is {0,1,2,3,.....}
however the set of integers and real numbers will be closed. The set of whole numbers are not closed because if b is large enough, a+a-b could be negative, and thus the result would not be an element of the whole numbers
You are given
So now think, if a = 2 and b = 3 now
The diamond symbol is not an operation in particular, just defined for this particualr problem.
Even easier