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High School Mathematics - 2
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 qp => q
TTT
TFF
FTT
FFT

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 qp <=> q
TTT
TFF
FTF
FFT

Regarding the truth values of p=>q and p<=>q, we have

  1. 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.
  2. The biconditional p<=>q is true whenever p and q have the same truth values, otherwise it is false.


Directions: Answer the following.