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logic homework 6: need help with logic hw all the instructions are on the document

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Philosophy 2310 Philosophy 2310 - Logic Problem Set 6 Check Blackboard for deadline. Late HW is not accepted. 1. For each of the following pairs of schemata, give an interpretation that shows that the first schema does not imply the second. (10 pts each) a) b) c) d) e) ("x)(\$y)Fxy (\$x)("y)Fxy • (\$x)("y)Fyx ("y)( (\$z)Fyz É (\$z)Fzy ) ("x)( ("y)(HyÉ~Fyx) É Hx ) (\$x)( (\$y)Gxy • ~(\$y)Gyx ) (\$x)(\$y)(Fxy • Fyx) (\$x)("y)(Fxy • Fyx) ("y)( ("z)Fyz É ("z)Fzy ) ("x)( (\$y)(Hy•~Fyx) É Hx ) (\$x)("y)(Gxy É Gyx) 2. For each of the following schemata. (i) (ii) Write two conservative instances, and Write down all of its non-conservative instances. If all of its instances are conservative, say so. (Make sure to say which instances are the conservative ones and which are the non-conservative ones.) In each case, what is the instantial variable? (10 pts each) a) b) c) d) e) (\$x)(Fxy • ~Fyx) ("z)(Gxz É ("x)(Fxz É Fyz)) ("x)(Fwxyz É ("w) (Gxww•Gxwx•Gxwy•Gxwz)) (\$w)("x)(Fxwx É ~Fwxw) (\$w)("x)(Fxwy É ~Fyxw) 1 ...
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