It is the property of => sign that c=>d is same as notd=>notc. Thus , you can replace notB=>notA by A=>B. Thus A iff B can be written as A=>B and B=>A . Of course what I am saying is same as what others have already said . I just wanted to emphasise how we can intuitively try to understand the logic from the meaning of 'if' and 'only if ...

2015年11月12日 · So I'm trying to come up with a simple explanation on the difference between if and iff, whilst also testing my understanding. Are these statements valid: X > 2 if X = 5 X= 5 iff X = 5

When A is sufficient for B, you say "if A then B" and write A => B. When both imply each other, you say "iff A then B" or "iff B then A" because implication is bidirectional and you write equivalence instead of implication, A <=> B. I think saying that things are equivalent is less confusing than iff. In

2010年11月15日 · What this implies depends on the logical system in place. If we have an appropriate De Morgan law for the logic, then we can infer ANCxyNCyx (at least one of either of the negation of one of the conditionals or the negation of the other conditional holds). But, that De Morgan law might not hold (and in fact doesn't hold for some logical systems).

2017年11月5日 · 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 ...

2016年3月9日 · Your answer had me the closest to understanding how to interpret iff, but I still feel as though I am missing something fundamental about two things implying one another. Due to the fact that I've been tossing around the previous definition for a while, I think it would be beneficial to look at a different example definition from Lara Alcock's ...

So, in Lukasiewicz 3-valued logic, the associativity of logical equivalence can take on the falsity value "0" and thus doesn't even qualify as a quasi-tautology (a quasi-tautology never takes on the value of falsity, the law of Clavius CCNppp comes as a quasi-tautology in Lukasiewicz 3 …

2020年12月26日 · $\begingroup$ I confirm; it is iff that in "common" math jargon is logical equivalence. The formula is not a formula of symbolic logic; thus, the bi-conditional connective is out of place there. But you have to remember that in classical logic $\varphi$ and $\psi$ are logically equivalent iff $\vDash \varphi \leftrightarrow \psi$ $\endgroup$

2015年7月9日 · $\begingroup$ @HagenvonEitzen Some think that the using "iff" in a definition is an unfortunate convention and that its not the same as the material bi-conditional. But, is it correct to say that the "if" part of the definition specifies the condition makes the new term applicable, and then the "only if" part says (now that the new term has ...

2020年11月28日 · $\begingroup$ My posts about the difference between $\equiv$ and $\iff$ and the difference between $\implies$ and $\rightarrow$ are apropos. Echoing the other commenters here with my usual caveat: "symbolic logic is an area rife with conflicting notation, terminology and even notions; my understanding is eclectically evolving."