See this https://gateoverflow.in/74921/multiplicative-inverse#c221200

'=' operator is used here too

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0 votes

+1 vote

It's a simple "If----then" statement.

Hence, the formulation would be of type $A \rightarrow B$

Here, $A$ is "xy=x for all y"...Or rephrasing, "For all y, xy = x"

Hence, $A$ = $\forall y (P(x,y,x))$

And $B$ is "$x = 0$"

So, "If xy=x for all y, then x =0" $\equiv$ $\forall y (P(x,y,x))$ $\rightarrow$ ($x = 0$)

You can check the above Propositional expression is Always True.

Hence, the formulation would be of type $A \rightarrow B$

Here, $A$ is "xy=x for all y"...Or rephrasing, "For all y, xy = x"

Hence, $A$ = $\forall y (P(x,y,x))$

And $B$ is "$x = 0$"

So, "If xy=x for all y, then x =0" $\equiv$ $\forall y (P(x,y,x))$ $\rightarrow$ ($x = 0$)

You can check the above Propositional expression is Always True.

0

See this https://gateoverflow.in/74921/multiplicative-inverse#c221200

'=' operator is used here too

0 votes

$\forall y\exists x\left (\left (P\left ( x ,y,z\right )=x\right )\rightarrow\left ( xy=x \right )\Lambda \left ( x=0 \right ) \right )$

0

= is just for the interpretation of statement

May be a bracket need to clear the statement "If xy=x for all y, then x =0."

May be a bracket need to clear the statement "If xy=x for all y, then x =0."

0

ultimately we need to get x as result and we are operating on function P(x,y,z) i.e. P(x,y,z)=x

and for that conditions are (xy=x) and (x=0)

I think it is resolution method http://nptel.ac.in/courses/106106140/39

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