USA: +1 (725) 712-1730 
Sign in
Explain why the logical negation (¬), conjunction (∧), and disjunction (∨) operators form a functionally complete collection of logical operators [Hint: think about the fact that we can construct logical expressions from truth tables as described above].
Need Short answer.
Expert Answer
Functionally complete set of logical operators is one which can be used to express all possible truth tables. Basically a well-known complete set of connectives is { v, ^, ¬}. Using these three logical operators, we can design all the logical operators (v, ^, ¬, -> , <=>).
Since the first three logical operators( v, ^, ¬ ) are already available, let us check for the remaining table.
let p and q be two statements.
p ->q is equivalent to ¬p ∨ q
p<=>q is equivalent to (¬p ∨ q) ∧ (¬q ∨ p) .
Using the three functionally complete logical operators, we can derive the whole logical operators present.
