Step 1: Understand the statement.
We are told $p\to(\sim p\lor q)$ is false and must find the truth values of $p$ and $q$.
Step 2: Recall when an implication is false.
An implication $A\to B$ is false only in one case: when $A$ is true and $B$ is false. Everywhere else it is true.
Step 3: Apply this here.
Here $A = p$ and $B = (\sim p\lor q)$. For the whole thing to be false we need $p$ true and $(\sim p\lor q)$ false.
Step 4: Set $p$ true.
If $p$ is true, then $\sim p$ is false.
Step 5: Make the OR false.
An OR statement $\sim p\lor q$ is false only when both parts are false. We already have $\sim p$ false, so we also need $q$ false.
Step 6: State the values.
So $p$ is true (T) and $q$ is false (F). \[ \boxed{p = \text{T},\ q = \text{F}} \]