Logical operators || and ! are all you need for every possible logical expression

I saw this on StackOverflow and thought it was a something we all ought to know!!!

Are || and ! operators sufficient to make every possible logical expression?

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[...] the set of operators comprising of || and ! isfunctionally complete. Here's a constructive proof of that, showing how to use them to express all sixteen possible logical connectives between the boolean variables A and B:

• True: A || !A
• A NAND B: !A || !B
• B implies A: !B || A
• A implies B: !A || B
• A OR B: A || B
• Not B: !B
• Not A: !A
• A XOR B: !(!A || B) || !(A || !B)
• A XNOR B: !(!A || !B) || !(A || B)
• A: A
• B: B
• A NOR B: !(A || B)
• A does not imply B: !(!A || B)
• B does not imply A: !(!B || A)
• A AND B: !(!A || !B)
• False: !(A || !A)

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See the fill answer here