The contrapositive of the statement "If you will work, you will earn money" is:
Show Hint
For a conditional statement "If p, then q" ($p \rightarrow q$):
- The converse is "If q, then p" ($q \rightarrow p$).
- The inverse is "If not p, then not q" ($\neg p \rightarrow \neg q$).
- The contrapositive is "If not q, then not p" ($\neg q \rightarrow \neg p$).
A statement and its contrapositive are always logically equivalent.
Let p be the statement "you will work".
Let q be the statement "you will earn money".
The given statement is in the form "If p, then q", which can be written symbolically as $p \rightarrow q$.
The contrapositive of a conditional statement $p \rightarrow q$ is $\neg q \rightarrow \neg p$.
First, find the negation of q ($\neg q$):
$\neg q$: "you will not earn money".
Next, find the negation of p ($\neg p$):
$\neg p$: "you will not work".
Now, form the contrapositive statement $\neg q \rightarrow \neg p$:
"If you will not earn money, then you will not work."
This matches option (C).
