Hi everyone

Im studying boolean algebra and one question is about checking functionally complete

Ive search a lot on the internet but still cant figure out how to do this.

Show { AND , <=> } is functionally incomplete

Can anyone give me some hints?

My idea is if we have a proposition which value is True

P | NOT P | P AND P | P<=> P

T F T T T T

we cant build a false using these operations, so it is not a functionally complete set

But how to do this in induction? Thank you