Consider the NAND operator $ uparrows, which is defined as follows $p uparrow q equiv eg (p wedge q)$ (1) (3 points) Using truth tables show that $ wedge$ is associative, i e , $p wedge (9 wedge r equiv(p wedge q) wedge r$ begin tabular ccc CCCC) $ mathrm p $ $ mathrm q $ $ mathrm r $ $(q wedge r$ $(p wedge (9 wedge r))$ $(p wedge 9)$ $((p wedge q) wedge r$ $(p wedge (9 wedger)) Leftrightarrow(p wedge q wedge r$ hline $ mathrm T $ $ mathrm T $ $ mathrm T $ 1 $ mathrm T $ $ mathrm T $ $ mathrm F $ $ mathrm T $ $ mathrm F $ $ mathrm T $ $ mathrm T $ $ mathrm F $ $ mathrm F $ $ mathrm F $ $ mathrm T $ $ mathrm T $ W $ mathrm F $ $ mathrm T $ $ mathrm F $ $ mathrm F $ $ mathrm F $ $ mathrm T $ W $ mathrm F $ $ mathrm F $ $ mathrm F $ end tabular) (2) (4 points) Using truth tables show that $ uparrow is not associative, i e , $p uparrow(q uparrow r ot equiv(p uparrow q) uparrow r$ CS PB 007

Question

Consider the NAND operator $ uparrows, which is defined as follows $p  uparrow q  equiv eg (p  wedge q)$  (1) (3 points) Using truth tables show that $ wedge$ is associative, i e , $p  wedge (9  wedge r  equiv(p  wedge q)  wedge r$   begin tabular  ccc  CCCC) $ mathrm p  $   $ mathrm q  $   $ mathrm r $   $(q wedge r$   $(p  wedge (9  wedge r))$   $(p  wedge 9)$   $((p  wedge q)  wedge r$   $(p wedge (9  wedger)) Leftrightarrow(p  wedge q  wedge r$  hline $ mathrm T $   $ mathrm T $   $ mathrm T $           1 $ mathrm T $   $ mathrm T $   $ mathrm F $         $ mathrm T $   $ mathrm F $   $ mathrm T $         $ mathrm T $   $ mathrm F $   $ mathrm F $         $ mathrm F $   $ mathrm T $   $ mathrm T $         W $ mathrm F $   $ mathrm T $   $ mathrm F $         $ mathrm F $   $ mathrm F $   $ mathrm T $         W $ mathrm F $   $ mathrm F  $   $ mathrm F  $          end tabular) (2) (4 points) Using truth tables show that $ uparrow is not associative, i e , $p  uparrow(q  uparrow r ot  equiv(p  uparrow q)  uparrow r$  CS PB  007

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Question

Consider the NAND operator $uparrows, which is defined as follows $p uparrow q equiv eg (p wedge q)$. (1) (3 points) Using truth tables show

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