#### Please [explain like I’m 5 years old](https://www.howtogeek.com/694298/what-does-eli5-mean-and-how-do-you-use-it), compare and contrast ALL 4 symbols =, ≡, ↔, ⇔.
All answers beneath are too knotty and byzantine to my secondary school daughter.
– https://math.stackexchange.com/q/500644
– https://math.stackexchange.com/q/3926367
– https://math.stackexchange.com/q/2432462
## https://math.stackexchange.com/q/4645583
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I think that maybe these explanations might be a bit hard to understand, and so I would like to make them simpler. Also, due to the close relationship between these four concepts, many people will tell you that some are the same as others when, in fact, they are not *quite* the same. It is not uncommon for this to be done in the classroom or in books on math and logic to simplify things, and it is quite possible that the distinction can be lost on, say, a teacher teaching the concepts. However, as these are stated as four distinct things I think that the nitpicky details are being asked for.
(1)= Equal Sign
This is equal to that. Example: 2+2=4
(2) ≡ Equivalence, Identity
If A ≡ B, then if A is true B is true and if A is false B is false. This is often described as “if and only if” and is sometimes written as iff. Example: You get $100 at the end of the semester ≡ Your GPA is over 3.5.
The next two can be a bit tricky as they are not always used exactly the same way in all math and logic. Additionally, both are forms of equivalence, and are thus often used interchangeably with equivalence and each other.
(3) ↔ Material BiConditional
This is used when two statements are connected together in equivalence, such that one is true if and only if the other is true at this time, but not necessarily at a different time or under different circumstances.
Example: Due to a snowstorm this morning (the material condition), Johnny cannot get to school from his house today unless his Dad drives him. Further, once there he will not be able to leave until the end of the school day.
Thus, “Johnny is at school” ↔ “Johnny was driven to school by his father this morning”.
On any other day, this may or may not be true, and thus this is material rather than logical.
(4) ⇔ Logical BiConditional
This is when two statements are connected together in equivalence such that one is true if and only if the other is true, period, regardless of any material conditions.
Example: A is equal to 4 ⇔ A is equal to 2+2. If the first part is true, then the second part is, and if the second part is not, neither is the first. No material changes can make that not the case, so it is a logical bi-conditional and not merely a material bi-conditional.
I tried to make this as clear and precise as possible. I hope it helps.
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