Changes

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%"

 

{| 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

|}

|}

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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&nbsp;(''p'',&nbsp;''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&nbsp;(''p'',&nbsp;''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%"

 

{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:60%"

|+ '''Conditional Operation : B &times; B &rarr; B'''

|+ '''Conditional Operation : B &times; B &rarr; 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

|}

|}

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