User:Anonymous Dissident/Math1

For $$(\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n) \in \left\{0,1\right\}$$
 * $$\mathrm{OR}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1-0^{\Omicron_1 + \dots + \Omicron_n}$$


 * $$\mathrm{NOR}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 0^{\Omicron_1+ \dots + \Omicron_n}$$


 * $$\mathrm{CONTRADICTION}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 0$$


 * $$\mathrm{TAUTOLOGY}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1$$


 * $$\mathrm{AND}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = \Omicron_1 \times \dots \times \Omicron_n$$


 * $$\mathrm{NAND}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1 - \Omicron_1 \times \dots \times \Omicron_n$$


 * $$\mathrm{XOR}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = |\Omicron_1 - |\Omicron_2 - | \dots - |\Omicron_{n-1} - \Omicron_n|||\dots|$$


 * $$\mathrm{XNOR}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1 - |\Omicron_1 - 1 - |\Omicron_2 - 1 - | \dots - |\Omicron_{n-1} - \Omicron_n|||\dots|$$


 * $$\mathrm{\Omicron_n}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = \Omicron_n$$


 * $$\mathrm{NOT\;\Omicron_n}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1 - \Omicron_n$$


 * $$\mathrm{MATERIAL\;NONIMPLICATION}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1\;-\;(0^{\Omicron_1 \times \dots \times \Omicron_{n-1}}\;+\;\Omicron_1 \times \dots \times \Omicron_n)$$


 * $$\mathrm{MATERIAL\;IMPLICATION}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 0^{\Omicron_1 \times \dots \times \Omicron_{n-1}}\;+\;\Omicron_1 \times \dots \times \Omicron_n$$


 * $$\mathrm{CONVERSE\;NONIMPLICATION}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 0^{\Omicron_1 + \dots + \Omicron_{n-1}}\;\times\;(\Omicron_1 + \dots +\Omicron_n)$$


 * $$\mathrm{CONVERSE\;IMPLICATION}[\Omicron_1,\Omicron_2,\Omicron_3, \dots ,\Omicron_n] = 1\;-\;0^{\Omicron_1 + \dots + \Omicron_{n-1}}\;\times\;(\Omicron_1 + \dots +\Omicron_n)$$