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## Homework Statement

Prove or disprove:

"If you can prove [tex] ( y \wedge \neg c ) \rightarrow Contradiction [/tex], then

[tex] y \rightarrow c [/tex] must be right."

## Homework Equations

My teacher used the sign [tex] \wedge [/tex], instead of [tex] \vee [/tex], like:

"If [tex]( a \wedge b \wedge \neg c ) \rightarrow Contradiction [/tex], then [tex] a \wedge b \rightarrow c [/tex] must be right."

I feel it is not right.

## The Attempt at a Solution

I proved in my replies:

"If you can prove [tex] ( a \wedge b \vee \neg c ) \rightarrow Contradiction [/tex], then

[tex] a \wedge b \rightarrow c [/tex] must be right."

I used the facts in my proof:

[tex] a \wedge \neg b = \neg ( a \rightarrow b ) = ( a \not \rightarrow b ) \not = \neg b \rightarrow \neg a \not = \neg a \not \rightarrow \neg b[/tex]

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