When a conditional statement and its converse are both true you can write it as a single biconditional statement.
Mary is in theater class if and only if she is in the fall play.
Practice makes perfect
When a conditional statement and its converse are both true, it can be rewritten as a single biconditional statement. If p is the hypothesis and q the conclusion, the biconditional statement is written as p if and only if q. From the exercise, we have been given both a hypothesis and a conclusion.
p&=Mary is in theater class
q&=she will be in the fall play
Using deductive reasoning, we know that both the conditional statement and converse is true. Therefore, we can write this as a biconditional statement.
Biconditional statement
Mary is in theater class if and only if
she is in the fall play.
