Fundamentals of Mathematics

If $$\displaystyle \left ( p\wedge \sim r \right )\Rightarrow \left ( q\vee r \right )$$ is false and $$q$$ and $$r$$ are both false, then $$p$$ is
"The reciprocal of focal length $$f$$ is equal to the sum of reciprocals of the object distance $$u$$ and the image distance $$v$$".
Make $$v$$ the subject of formula, obtained above
$$\left [ p\wedge (\sim q) \right ]\wedge \left [ (\sim p)\vee q \right ]$$ is
The conjunction of statement: "Mumbai is a city, it is not the capital city."
Using PMI, prove that $${3^{2n + 2}} - 8n - 9$$ is divisible by $$64$$.