Mixing
is iff the same as equiv? When to use which?
$begingroup$
Is there a difference between using $iff$(iff) and $equiv$ (equiv)?
When should I use one or the other?
logic
asked Nov 5 '17 at 20:43
JoStackJoStack
153
$endgroup$
add a comment |
$begingroup$
Is there a difference between using $iff$(iff) and $equiv$ (equiv)?
When should I use one or the other?
logic
asked Nov 5 '17 at 20:43
JoStackJoStack
153
$endgroup$
1
$begingroup$
What about $leftrightarrow$?
$endgroup$
– Hagen von Eitzen
Nov 5 '17 at 20:45
add a comment |
$begingroup$
Is there a difference between using $iff$(iff) and $equiv$ (equiv)?
When should I use one or the other?
logic
asked Nov 5 '17 at 20:43
JoStackJoStack
153
$endgroup$
Is there a difference between using $iff$(iff) and $equiv$ (equiv)?
When should I use one or the other?
logic
logic
asked Nov 5 '17 at 20:43
JoStackJoStack
153
asked Nov 5 '17 at 20:43
JoStackJoStack
153
asked Nov 5 '17 at 20:43
JoStackJoStack
153
asked Nov 5 '17 at 20:43
JoStackJoStack
153
asked Nov 5 '17 at 20:43
JoStackJoStack
153
153
1
$begingroup$
What about $leftrightarrow$?
$endgroup$
– Hagen von Eitzen
Nov 5 '17 at 20:45
add a comment |
1
$begingroup$
What about $leftrightarrow$?
$endgroup$
– Hagen von Eitzen
Nov 5 '17 at 20:45
1
1
$begingroup$
What about $leftrightarrow$?
$endgroup$
– Hagen von Eitzen
Nov 5 '17 at 20:45
$begingroup$
What about $leftrightarrow$?
$endgroup$
– Hagen von Eitzen
Nov 5 '17 at 20:45
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Unfortunately there does not seem to be a strict rule (or even all that great of a consensus) as to what symbol to use where and when. The most important thing is that you understand the difference between a logic symbol and a meta-logic symbol:
The material biconditional is a truth-function that takes two logic expressions and combines them into a new one. As such, it is part of a logic statement. You often see $P leftrightarrow Q$, but some books use $P equiv Q$, and some use $P Leftrightarrow Q$
On the other hand, logical equivalence is a statement about two logic statements, namely that they have the same truth-conditions. We know, for example, that the logic statement $neg (P lor Q)$ is logically equivalent to $neg P land neg Q$. We can write a symbol between them to say this about them, but as such we don't get a new logic statement, but rather a meta-logical statement. For this, I can't recall ever having seen the $leftrightarrow$ used, but you'll see both $neg (P lor Q) equiv neg P land neg Q$ and $neg (P lor Q) Leftrightarrow neg P land neg Q$. I've also seen $neg (P lor Q) :: neg P land neg Q$
Anyway, context should make it clear what is meant by which symbol, and which symbol you are therefore supposed to use.
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
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add a comment |
$begingroup$
Let's take a look at the definition from Rosen's Discrete Mathematics and its Applications.
Definition:
The compound propositions $p$ and $q$ are called logically equivalent if $p iff q$ is a tautology. The notation $p equiv q$ denotes that $p$ and $q$ are logically equivalent.
That is, the symbol $equiv$ is not a logical connective, and $p equiv q$ is not a compound proposition but rather is the statement that $p iff q$ is a tautology.
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
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2 Answers
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2 Answers
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$begingroup$
Unfortunately there does not seem to be a strict rule (or even all that great of a consensus) as to what symbol to use where and when. The most important thing is that you understand the difference between a logic symbol and a meta-logic symbol:
The material biconditional is a truth-function that takes two logic expressions and combines them into a new one. As such, it is part of a logic statement. You often see $P leftrightarrow Q$, but some books use $P equiv Q$, and some use $P Leftrightarrow Q$
On the other hand, logical equivalence is a statement about two logic statements, namely that they have the same truth-conditions. We know, for example, that the logic statement $neg (P lor Q)$ is logically equivalent to $neg P land neg Q$. We can write a symbol between them to say this about them, but as such we don't get a new logic statement, but rather a meta-logical statement. For this, I can't recall ever having seen the $leftrightarrow$ used, but you'll see both $neg (P lor Q) equiv neg P land neg Q$ and $neg (P lor Q) Leftrightarrow neg P land neg Q$. I've also seen $neg (P lor Q) :: neg P land neg Q$
Anyway, context should make it clear what is meant by which symbol, and which symbol you are therefore supposed to use.
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
$endgroup$
add a comment |
$begingroup$
Unfortunately there does not seem to be a strict rule (or even all that great of a consensus) as to what symbol to use where and when. The most important thing is that you understand the difference between a logic symbol and a meta-logic symbol:
The material biconditional is a truth-function that takes two logic expressions and combines them into a new one. As such, it is part of a logic statement. You often see $P leftrightarrow Q$, but some books use $P equiv Q$, and some use $P Leftrightarrow Q$
On the other hand, logical equivalence is a statement about two logic statements, namely that they have the same truth-conditions. We know, for example, that the logic statement $neg (P lor Q)$ is logically equivalent to $neg P land neg Q$. We can write a symbol between them to say this about them, but as such we don't get a new logic statement, but rather a meta-logical statement. For this, I can't recall ever having seen the $leftrightarrow$ used, but you'll see both $neg (P lor Q) equiv neg P land neg Q$ and $neg (P lor Q) Leftrightarrow neg P land neg Q$. I've also seen $neg (P lor Q) :: neg P land neg Q$
Anyway, context should make it clear what is meant by which symbol, and which symbol you are therefore supposed to use.
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
$endgroup$
add a comment |
$begingroup$
Unfortunately there does not seem to be a strict rule (or even all that great of a consensus) as to what symbol to use where and when. The most important thing is that you understand the difference between a logic symbol and a meta-logic symbol:
The material biconditional is a truth-function that takes two logic expressions and combines them into a new one. As such, it is part of a logic statement. You often see $P leftrightarrow Q$, but some books use $P equiv Q$, and some use $P Leftrightarrow Q$
On the other hand, logical equivalence is a statement about two logic statements, namely that they have the same truth-conditions. We know, for example, that the logic statement $neg (P lor Q)$ is logically equivalent to $neg P land neg Q$. We can write a symbol between them to say this about them, but as such we don't get a new logic statement, but rather a meta-logical statement. For this, I can't recall ever having seen the $leftrightarrow$ used, but you'll see both $neg (P lor Q) equiv neg P land neg Q$ and $neg (P lor Q) Leftrightarrow neg P land neg Q$. I've also seen $neg (P lor Q) :: neg P land neg Q$
Anyway, context should make it clear what is meant by which symbol, and which symbol you are therefore supposed to use.
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
$endgroup$
Unfortunately there does not seem to be a strict rule (or even all that great of a consensus) as to what symbol to use where and when. The most important thing is that you understand the difference between a logic symbol and a meta-logic symbol:
The material biconditional is a truth-function that takes two logic expressions and combines them into a new one. As such, it is part of a logic statement. You often see $P leftrightarrow Q$, but some books use $P equiv Q$, and some use $P Leftrightarrow Q$
On the other hand, logical equivalence is a statement about two logic statements, namely that they have the same truth-conditions. We know, for example, that the logic statement $neg (P lor Q)$ is logically equivalent to $neg P land neg Q$. We can write a symbol between them to say this about them, but as such we don't get a new logic statement, but rather a meta-logical statement. For this, I can't recall ever having seen the $leftrightarrow$ used, but you'll see both $neg (P lor Q) equiv neg P land neg Q$ and $neg (P lor Q) Leftrightarrow neg P land neg Q$. I've also seen $neg (P lor Q) :: neg P land neg Q$
Anyway, context should make it clear what is meant by which symbol, and which symbol you are therefore supposed to use.
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
edited Nov 5 '17 at 21:02
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
answered Nov 5 '17 at 20:55
Bram28Bram28
62.1k44793
62.1k44793
add a comment |
add a comment |
$begingroup$
Let's take a look at the definition from Rosen's Discrete Mathematics and its Applications.
Definition:
The compound propositions $p$ and $q$ are called logically equivalent if $p iff q$ is a tautology. The notation $p equiv q$ denotes that $p$ and $q$ are logically equivalent.
That is, the symbol $equiv$ is not a logical connective, and $p equiv q$ is not a compound proposition but rather is the statement that $p iff q$ is a tautology.
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
$endgroup$
add a comment |
$begingroup$
Let's take a look at the definition from Rosen's Discrete Mathematics and its Applications.
Definition:
The compound propositions $p$ and $q$ are called logically equivalent if $p iff q$ is a tautology. The notation $p equiv q$ denotes that $p$ and $q$ are logically equivalent.
That is, the symbol $equiv$ is not a logical connective, and $p equiv q$ is not a compound proposition but rather is the statement that $p iff q$ is a tautology.
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
$endgroup$
add a comment |
$begingroup$
Let's take a look at the definition from Rosen's Discrete Mathematics and its Applications.
Definition:
The compound propositions $p$ and $q$ are called logically equivalent if $p iff q$ is a tautology. The notation $p equiv q$ denotes that $p$ and $q$ are logically equivalent.
That is, the symbol $equiv$ is not a logical connective, and $p equiv q$ is not a compound proposition but rather is the statement that $p iff q$ is a tautology.
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
$endgroup$
Let's take a look at the definition from Rosen's Discrete Mathematics and its Applications.
Definition:
The compound propositions $p$ and $q$ are called logically equivalent if $p iff q$ is a tautology. The notation $p equiv q$ denotes that $p$ and $q$ are logically equivalent.
That is, the symbol $equiv$ is not a logical connective, and $p equiv q$ is not a compound proposition but rather is the statement that $p iff q$ is a tautology.
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
answered Jan 12 at 2:44
ShinobuIsMyWifeShinobuIsMyWife
183
183
add a comment |
add a comment |
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$begingroup$
What about $leftrightarrow$?
$endgroup$
– Hagen von Eitzen
Nov 5 '17 at 20:45