Is the converse to the conditional statement true?
Your sister is right, see solution.
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 is 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&=I bought a shirt
q&=I went to the mall
Assuming that shirts are only sold at the mall, the conditional statement your friend uttered is true. To write this as a biconditional statement, we must examine the converse of this statement.
If I went to the mall,
then I bought a shirt
This is not a true statement — just because you go to the mall, you do not have to buy a shirt. Therefore, you sister is right. You cannot write this as a biconditional statement.
