I understand that showing function completeness is to use the symbols to generate the same truth values as if the other symbol would allow.
Out of the symbols {∧,∨,→,↔}, how would you generate the negation symbol '¬'
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1Not possible; you need the False : $\bot$ constant. – Mauro ALLEGRANZA Sep 04 '19 at 06:38
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Thanks @MauroALLEGRANZA. Is any longer justification to this. I can see that using those symbols, if you made a truth table, you can't ever make it false when its premises are true – D.Ronald Sep 04 '19 at 06:44
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See Lila Kari, Adequate set of connectives. – Mauro ALLEGRANZA Sep 04 '19 at 06:47
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The problem was solved by Post (1921). – Mauro ALLEGRANZA Sep 04 '19 at 14:39