BTGmoderatorDC wrote:If n is an integer, is n even?
(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.
Source: Official Guide
\[n\,\,\operatorname{int} \,\,\,\,\left( { \Rightarrow \,\,\,n\,\,{\text{odd}}\,\,{\text{or}}\,\,n\,\,{\text{even}}\,,\,\,{\text{and}}\,\,{\text{not}}\,\,{\text{both}}} \right)\,\,\,\,\,\,\,\,\,\left( * \right)\]
\[n\,\,\mathop = \limits^? \,\,{\text{even}}\]
\[\left( 1 \right)\,\,\,{n^2} - 1\,\,\,{\text{odd}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{{\text{n}}^{\text{2}}}\,\,\,{\text{even}}\,\,\,\,\mathop \Rightarrow \limits_{n\,\,{\text{not}}\,\,{\text{odd}}}^{\left( * \right)} \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
\[\left( 2 \right)\,\,\,3n + 4\,\,\,{\text{even}}\,\,\,\,\, \Rightarrow \,\,\,\,\,3n\,\,\,{\text{even}}\,\,\,\,\mathop \Rightarrow \limits_{n\,\,{\text{not}}\,\,{\text{odd}}}^{\left( * \right)} \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
