| द्विदिशा दुविधा | अगर क तो श; और अगर त तो र ; लेकिन क या र नहीं ; उसलिए श या त नहीं | |
| सरलीकरण | क और श सत्य हैं ; उसलिए क सत्य हैं | |
| संयोजन | क और श अलग अलग सत्य हैं ; therefore they are true conjointly | ये क हैं , ये श हैं , इसलिए दोनों को जोड़ना हैं |
| जोड़ना | p is true; therefore the disjunction (p or q) is true | क्ष से या तो क निकलो या श निकलो पर दोनों नही |
| सम्मिश्रित | अगर क तो श; and if p then r; therefore if p is true then q and r are true | क * (श + ष ) = क * श + क * ष |
| De Morgan's Theorem (1) | The negation of (p and q) is equiv. to (not p or not q) | |
| De Morgan's Theorem (2) | The negation of (p or q) is equiv. to (not p and not q) | |
| विनिमय (1) | (p or q) is equiv. to (q or p) | क * श = श * क |
| विनिमय (2) | (p and q) is equiv. to (q and p) | क * श = श * क |
| विनिमय (3) | (p is equiv. to q) is equiv. to (q is equiv. to p) | क * श = श * क |
| संगठन (1) | p or (q or r) is equiv. to (p or q) or r | क * (श * ष ) = श * ( क * ष ) |
| संगठन (2) | p and (q and r) is equiv. to (p and q) and r | क * (श + ष ) = क * श + क * ष |
| वितरण (1) | p and (q or r) is equiv. to (p and q) or (p and r) | |
| वितरण (2) | p or (q and r) is equiv. to (p or q) and (p or r) | |
| दोबारा नकारना | p is equivalent to the negation of not p | |
| स्थानांतरण | अगर क तो श is equiv. to if not q then not p | |
| वस्तुगत निहितार्थ | अगर क तो श is equiv. to not p or q | |
| वस्तुगत समानक (1) | (p iff q) is equiv. to (if p is true then q is true) and (if q is true then p is true) | |
| वस्तुगत समानक (2) | (p iff q) is equiv. to either (p and q are true) or (both p and q are false) | |
| वस्तुगत समानक (3) | (p iff q) is equiv to., both (p or not q is true) and (not p or q is true) | |
| Exportation[12] | from (if p and q are true then r is true) we can prove (if q is true then r is true, if p is true) | |
| Importation | If p then (if q then r) is equivalent to if p and q then r | |
| Tautology (1) | p is true is equiv. to p is true or p is true | |
| Tautology (2) | p is true is equiv. to p is true and p is true | |
| Tertium non datur (Law of Excluded Middle) | p or not p is true | |
| Law of Non-Contradiction | p and not p is false, is a true statement | |
Discussion