#### 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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= is used to signify two numerical quantities are equal. 5=6-1.
≡ is used in lieu of “is the same as”, verbally speaking. It denotes identities, i.e. two expressions whose value is equal no matter what the variables are. For example: (a+b)^2 ≡ a^2 + 2ab + b^2 . In most cases, we simply use = instead, but it is important to remember that it’s simply an equivalence sign.
Do note that ≡ is more frequently used to denote **congruence**. Two numbers are congruent modulo a number N if N divides their difference. We write a ≡ b (mod n).
⇔ is “if and only if”. P ⇔ Q means Q is true if and only if P is true. The truth table for this condition is such that P ⇔ Q is true in two cases: both P and Q are true, or both P and Q are false. This logical equivalence **can also be written**, albeit less frequently, as P ≡ Q
↔ is used exactly the same way as ⇔. No difference whatsoever.
Summary: It’s better to learn these symbols as part of the required reading, there sometimes is significant overlap between what they are used for.
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