Validity - Preservation

Preservation

In truth-preserving validity, the interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true'.

In a false-preserving validity, the interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false'.

Preservation properties Logical connective sentences
True and false preserving: Logical conjunction (AND, ) • Logical disjunction (OR, )
True preserving only: Tautology ( ) • Biconditional (XNOR, ) • Implication ( ) • Converse implication ( )
False preserving only: Contradiction ( ) • Exclusive disjunction (XOR, ) • Nonimplication ( ) • Converse nonimplication ( )
Non-preserving: Proposition • Negation ( ) • Alternative denial (NAND, ) • Joint denial (NOR, )

Read more about this topic:  Validity

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