12,080
edits
Changes
table colors → table body (#f8f8ff = ghostwhite) table head (#e6e6ff = blue gray)
In the interpretation where <math>0 = \mathrm{false}</math> and <math>1 = \mathrm{true}</math>, the truth table associated with the statement "<math>p</math> implies <math>q</math>", symbolized as <math>p \Rightarrow q</math>, is as follows:
In the interpretation where <math>0 = \mathrm{false}</math> and <math>1 = \mathrm{true}</math>, the truth table associated with the statement "<math>p</math> implies <math>q</math>", symbolized as <math>p \Rightarrow q</math>, is as follows:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:45%"
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
|+ '''Logical Implication'''
|+ '''Logical Implication'''
|- style="background:paleturquoise"
|- style="background:#e6e6ff"
! style="width:15%" | p
! style="width:15%" | p
! style="width:15%" | q
! style="width:15%" | q
| 1 || 1 || 1
| 1 || 1 || 1
|}
|}
<br>
<br>
The main formal object under discussion is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' just in case the first operand is true and the second operand is false. By way of a temporary name, the logical operation in question may be written as Cond (''p'', ''q''), where ''p'' and ''q'' are logical values. The [[truth table]] associated with this operation is as follows:
The main formal object under discussion is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' just in case the first operand is true and the second operand is false. By way of a temporary name, the logical operation in question may be written as Cond (''p'', ''q''), where ''p'' and ''q'' are logical values. The [[truth table]] associated with this operation is as follows:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:60%"
|+ '''Conditional Operation : B × B → B'''
|+ '''Conditional Operation : B × B → B'''
|- style="background:paleturquoise"
|- style="background:#e6e6ff"
! style="width:15%" | p
! style="width:15%" | p
! style="width:15%" | q
! style="width:15%" | q
| T || T || T
| T || T || T
|}
|}
<br>
<br>