Logic Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! ====Truth tables==== [[Truth table]]s can be used to show how logical connectives work or how the truth values of complex propositions depends on their parts. They have a column for each input variable. Each row corresponds to one possible combination of the truth values these variables can take; for truth tables presented in the English literature, the symbols "T" and "F" or "1" and "0" are commonly used as abbreviations for the truth values "true" and "false".{{sfnm|1a1=Magnus|1y=2005|1loc=3. Truth tables|1pp=35β38|2a1=Angell|2y=1964|2p=164|3a1=Hall|3a2=O'Donnell|3y=2000|3p=[https://books.google.com/books?id=yP4MJ36C4ZgC&pg=PA48 48]}} The first columns present all the possible truth-value combinations for the input variables. Entries in the other columns present the truth values of the corresponding expressions as determined by the input values. For example, the expression {{nowrap|"<math>p \land q</math>"}} uses the logical connective <math>\land</math> ([[Logical conjunction|and]]). It could be used to express a sentence like "yesterday was Sunday and the weather was good". It is only true if both of its input variables, <math>p</math> ("yesterday was Sunday") and <math>q</math> ("the weather was good"), are true. In all other cases, the expression as a whole is false. Other important logical connectives are <math>\lnot</math> ([[Negation|not]]), <math>\lor</math> ([[Logical disjunction|or]]), <math>\to</math> ([[Material conditional|if...then]]), and <math>\uparrow</math> ([[Sheffer stroke]]).{{sfnm|1a1=Magnus|1y=2005|1loc=3. Truth tables|1pp=35β45|2a1=Angell|2y=1964|2p=164}} Given the conditional proposition {{nowrap|<math>p \to q</math>}}, one can form truth tables of its [[Converse (logic)|converse]] {{nowrap|<math>q \to p</math>}}, its [[Inverse (logic)|inverse]] {{nowrap|(<math>\lnot p \to \lnot q</math>)}}, and its [[contrapositive (logic)|contrapositive]] {{nowrap|(<math>\lnot q \to \lnot p</math>)}}. Truth tables can also be defined for more complex expressions that use several propositional connectives.{{sfn |Tarski |1994 |p=40}} {| class="wikitable" style="margin:1em; text-align:center;" |+ Truth table of various expressions |- ! style="width:15%" | ''p'' ! style="width:15%" | ''q'' ! style="width:15%" | ''p'' β§ ''q'' ! style="width:15%" | ''p'' β¨ ''q'' ! style="width:15%" | ''p'' β ''q'' ! style="width:15%" | ''Β¬p'' β ''Β¬q'' ! style="width:15%" | ''p'' <math>\uparrow</math> ''q'' |- | T || T || T || T || T || T || style="background:papayawhip" | F |- | T || style="background:papayawhip" | F || style="background:papayawhip" | F || T || style="background:papayawhip" | F || T || T |- | style="background:papayawhip" | F || T || style="background:papayawhip" | F || T || T || style="background:papayawhip" | F || T |- | style="background:papayawhip" | F || style="background:papayawhip" | F || style="background:papayawhip" | F || style="background:papayawhip" | F || T || T || T |} Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page