what does the star symbol means in binary operation algebra (logic) Does it refer to a certain rule
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Note $1+xy = (1+x)(1+y)$ so the "" operation is isomorphic to multiplication. – Somos Jan 07 '18 at 03:25
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The votes to close surprise me. I think this is a reasonable question for someone new to abstract algebra. It's posed clearly and directly. – Ethan Bolker Jan 07 '18 at 13:41
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Its ok and i think that it is clear enough anyway thanxs ✋ – Issa Faour Jan 08 '18 at 23:03
4 Answers
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It means the operation defined on the RHS.
For example $$2*3= 2+ 3+2\times 3=11$$
velut luna
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1I think using the same star for both the defined operation and multiplication is a bit confusing. – Logan Clark Jan 07 '18 at 01:55
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No.
In your example $x*y$ is being defined to mean the binary operation: $x+y+xy$. (Presumably so you can solve some problem about such a binary operation.)
In another problem you might be told $x*y$ means something else. Or in general we can say "Let $*$ be a binary operation" and we won't know anything about what $x*y$ is; just that it is some binary operation.
fleablood
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I doesn't refer to a certain rule, it refers to the particular rule defined at the moment.
Ethan Bolker
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In binary logic $+$ refers to OR and $\cdot$ refers to AND.
You could also use alternate notation $x\lor y\lor(x\land y)$ but it is equivalent to simple $x\lor y$ or $x+y$ in the origninal notation.
Assuming it is really a logical operation, I do not see the purpose of defining $*$ if it is the same thing as $+$ or maybe this is th epurpose of the exercise to show they are the same rules.
Anyway, I sometimes saw $*$ being used for NAND i.e. $\lnot(x\land y)$ or $(xy)'$ in both notations.
But this is not the case here, are you certain about the definition of $x*y$ ?
zwim
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