High School Mathematics - 2 14.3 Conditional Statements
We frequently come across statements like:
"If p then q" are called conditional statements and denoted as p=>q and read as p implies q.
Truth table for a conditional
p
q
p => q
T
T
T
T
F
F
F
T
T
F
F
T
A statement of the form "p if and only if q" are called biconditional statements and are denoted by p<=>q. Biconditional Statement Truth table for a biconditional
p
q
p <=> q
T
T
T
T
F
F
F
T
F
F
F
T
Regarding the truth values of p=>q and p<=>q, we have
The conditional p=>q is false only if p is true and q is false. Accordingly, if p is false, then p=>q is true regardless of the truth value of q.
The biconditional p<=>q is true whenever p and q have the same truth values, otherwise it is false.