Editing Propositional formula (section)

=== Connectives of rhetoric, philosophy and mathematics ===
The following are the connectives common to rhetoric, philosophy and mathematics together with their [[truth table]]s. The symbols used will vary from author to author and between fields of endeavor. In general the abbreviations "T" and "F" stand for the evaluations TRUTH and FALSITY applied to the variables in the propositional formula (e.g. the assertion: "That cow is blue" will have the truth-value "T" for Truth or "F" for Falsity, as the case may be.).

The connectives go by a number of different word-usages, e.g. "a IMPLIES b" is also said "IF a THEN b". Some of these are shown in the table.

{|class="wikitable"
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| width="45" | 
| width="42" | 
| width="60" | 
| width="57.75" | 
|style="background-color:#E5E0EC" width="114.75" | b only if a
| width="187.5" | 
| width="93" | 
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|style="background-color:#E5E0EC" | b IS SUFFICIENT FOR a
|style="background-color:#F2F2F2" | b PRECISELY WHEN a
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|style="background-color:#E5E0EC" | {{not a typo|a}} IS NECESSARY FOR b
|style="background-color:#F2F2F2" | b IF AND ONLY IF a;  b IFF a
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|- style="font-size:9pt" align="center"
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|style="background-color:#FDE9D9" | inclusive OR
|style="background-color:#E5E0EC" | IF b THEN a
|style="background-color:#F2F2F2" | b IS NECESSARY AND SUFFICIENT FOR a
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|style="background-color:#EAF1DD" | negation
|style="background-color:#EAF1DD" | negation
|style="background-color:#DBE5F1" | conjunction
|style="background-color:#FDE9D9" | disjunction
|style="background-color:#E5E0EC" | implication
|style="background-color:#F2F2F2" | biconditional
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|- style="font-size:9pt" align="center"
! Height="12" colspan="2" | variables
|style="background-color:#EAF1DD" | NOT b
|style="background-color:#EAF1DD" | NOT a
|style="background-color:#DBE5F1" | b AND a
|style="background-color:#FDE9D9" | b OR a
|style="background-color:#E5E0EC" | b IMPLIES a
|style="background-color:#F2F2F2" | b IS [[Logical equivalence|logically equivalent]] TO a ***
| f IS A tautology
| NEITHER a NOR b
| b stroke a
| exclusive OR
|- style="font-size:9pt" align="center"
|style="font-weight:bold" Height="12" | b
|style="font-weight:bold" | a
|style="background-color:#EAF1DD;font-weight:bold" | &not;(b)
|style="background-color:#EAF1DD;font-weight:bold" | &not;(a)
|style="background-color:#DBE5F1;font-weight:bold" | (b &and; a)
|style="background-color:#FDE9D9;font-weight:bold" | (b &or; a)
|style="background-color:#E5E0EC;font-weight:bold" | (b → a)
|style="background-color:#F2F2F2;font-weight:bold" | (b ↔ a)
| (f = formula)
| (a NOR b)
|style="font-weight:bold" | (b|a)
|style="font-weight:bold" | various
|-  align="center"
| Height="12" | F
| F
|style="background-color:#EAF1DD" | T
|style="background-color:#EAF1DD" | T
|style="background-color:#DBE5F1" | F
|style="background-color:#FDE9D9" | F
|style="background-color:#E5E0EC;font-size:9pt" | T
|style="background-color:#F2F2F2;font-size:9pt" | T
|style="font-size:9pt" | T
|style="font-size:9pt" | T
| T
|style="font-size:9pt" | F
|-  align="center"
| Height="12" | F
|style="font-size:9pt" | T
|style="background-color:#EAF1DD" | T
|style="background-color:#EAF1DD;font-size:9pt" | F
|style="background-color:#DBE5F1" | F
|style="background-color:#FDE9D9;font-size:9pt" | T
|style="background-color:#E5E0EC;font-size:9pt" | T
|style="background-color:#F2F2F2;font-size:9pt" | F
|style="font-size:9pt" | T
|style="font-size:9pt" | F
| T
|style="font-size:9pt" | T
|-  align="center"
|style="font-size:9pt" Height="12" | T
| F
|style="background-color:#EAF1DD" | F
|style="background-color:#EAF1DD" | T
|style="background-color:#DBE5F1" | F
|style="background-color:#FDE9D9;font-size:9pt" | T
|style="background-color:#E5E0EC;font-size:9pt" | F
|style="background-color:#F2F2F2;font-size:9pt" | F
|style="font-size:9pt" | T
|style="font-size:9pt" | F
| T
|style="font-size:9pt" | T
|-  align="center"
|style="font-size:9pt" Height="12" | T
|style="font-size:9pt" | T
|style="background-color:#EAF1DD" | F
|style="background-color:#EAF1DD;font-size:9pt" | F
|style="background-color:#DBE5F1;font-size:9pt" | T
|style="background-color:#FDE9D9;font-size:9pt" | T
|style="background-color:#E5E0EC;font-size:9pt" | T
|style="background-color:#F2F2F2;font-size:9pt" | T
|style="font-size:9pt" | T
|style="font-size:9pt" | F
|style="font-size:9pt" | F
|style="font-size:9pt" | F
|}