Conditional/Bi-Conditional Laws

 Conditonal Law:

This law is also known as Law of Inference or Implication. For any 2 binary values P & Q, it represents the "If P then Q" relationship.

which means that for any set of truth values, if P is true than Q should be true to generate a true result otherwise it will give you false. Rest other cases will be true.

This law is represented as :

P→ Q           If P, then Q, here P is known as "Antecedent" & Q as "Consequence"
OR
P⇒ Q
OR
P ⊃ Q

It can be algebrically represented as P'+Q,.

Same can be seen in the following truth table that when P=1 & Q=0 then, P→Q results in 0(False), rest all cases are 1(True).

P	Q	P→Q
0	0	1
0	1	1
1	0	0
1	1	1

Bi-Conditional Law:

This law is also known as Law of Equivalence. For any 2 binary values P & Q, it represents the "If and only if " relationship.

which means that for any set of truth values, if and only if both are same than it generates a True result. Rest other cases will be False.

This law is represented as :

P↔Q           If and only if both are same

OR
P⇔Q

OR
P ≡ Q

It can be algebrically represented as P'Q' + PQ

Same can be seen in the following truth table that when P=0 & Q=0 OR when P=1 & Q=1

then P⇔Q results in 1(True), rest all cases are 0(False).

P	Q	P⇔Q
0	0	1
0	1	0
1	0	0
1	1	1