Biconditional Statements | 'if and only if'

A biconditional statement is one of the form "if and only if", sometimes written as "iff". The statement "p if and only if q" means "p implies q" AND "q implies p". That is, it is a conjunction of two individual conditional statements. In this video we will see how to write and interpret sentences using if and only if notation.

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[hummah]

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[SassePhoto]

If and only if I listen carefully to this excellent video then I will understand the logic of if and only

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[thomasdrew]

Thank you for the informative videos! They are incredibly helpful. I just wanted to point out that the title of this video says "Bionditional" instead of "Biconditional" but we all knew what you meant. ;)

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[saityusufbulur]

We can think of the difference between conditional and biconditional as follows.

"If I study hard, then I will pass the exam" means

"If I list the possible reasons for passing the exam, "studying hard" is 100% included in that list. This is not the only reason, but it is one reason."

On the other hand, "I will pass the exam if and only if I study hard" means

"In the list of possible reasons for passing the exam, there's only one element, and it is "studying hard". There is no other reason."

[MrMemeDuck]

Thank you!!! This really helps clear things up and super concisely too!

[nekomaru]

Note, "if and only if" -> iff. (shorthand)↔⇔≡⟺

[kobbygbena]

I really appreciate this great content but, i think adding its truth table would've been super.

[IsaAbuhuseina]

Can anyone please answer this question for me? I'm really confused!
Q. For an implication "p implies q", if "q" becomes hypothesis and "p" becomes conclusion, then it is of
the given implication "p implies q".

[burgerwithcheese]

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