α c β ≈ (avb) ^ -(a^b)
a c b ≈ -(a^-b)^-(a^b)
a c b ≈ -(-(avb)v-(-av-b)))
taken together, ^, v and – are expressively adequate (functionally complete) in metalogic.
((a^b) ^ g) ≈ (a^(b^g)
There exists a simple one-to-one correspondence between
valuation over n wff’s
conjunctions with n conjuncts
for example, consider the atoms P, Q and R
P:=1 Q:=1 R:=1
P^Q
P:=1 Q:=0 R:=1
P^-Q
These are called basic conjunctions.
With basic connections we can forumalise any other logical formula solely based on truth table valuations and variables.