Biconditionals  Logic
Biconditionals
Lessons
Notes:
A biconditional is a conjunction of a conditional and its converse. In symbolic form it would be:
$(p \to q)$ ˄ $(q \to p)$
We can also write it as $p \leftrightarrow q$. In words, we connect $p$ and $q$ with "if and only if". A biconditional can be only true if both the conditional and converse is true. Here is a truth table of a biconditional.
$p$  $q$  $p \to q$  $q \to p$  $(p \to q )$ ˄ $(q \to p)$  $p \leftrightarrow q$ 
T  T  T  T  T  T 
T  F  F  T  F  F 
F  T  T  F  F  F 
F  F  T  T  T  T 

a)
What are Biconditionals


1.
Forming the Biconditional
Write a biconditional using the given conditionals: 
2.
You are given 3 statements in symbolic form:
$p$: There is cream in milk
$q$: There is milk in coffee
$r$: There is cream in coffee 
3.
Truth value of Biconditionals
Determine the truth value of the following biconditionals: 
4.
Let both $p$, $q$ and $r$ be statements.