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Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this $on\; z^+,define\; \ast by \;a\;\ast\; b=ab.$

Note: This is part 2 of a 5 part question, split as 5 separate questions here.
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1 Answer

  • A binary operation $∗$ on a set $A$ is a function $∗$ from $A \times A$ to $ A$. Therefore, if $a,b \in A \Rightarrow a*b \in A\; \forall\; a,b, \in A$
Given On $Z^+,*$ is defined by $a*b=ab$
It means that for each $a,b \in Z^+$, there is a unique element $ab \in Z^+$. This is true because the product of two numbers is also postive. Therefore $*$ operation defined here must be a binary operation.as it defines a unique element $a*b = ab \in Z^+$.
answered Mar 13, 2013 by sreemathi.v
edited Mar 19, 2013 by balaji.thirumalai

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