Propositions

Let $p,q,$ and $r$ denote the following propositions:

$p$ denotes "You passed CS$2233"$

$q$ denotes "You passed CS$3333"$

$r$ denotes "You can register for CS$3343"$

$s$ denotes "You understand boolean algebra"

Using $p,q,$ and $r$ construct compound propositions which represent the following English sentences:

$(1)(10$ pts$)(10$ pts$)$You haven't passed CS$2233$ but you understand boolean algebra.

$(2)(10$ pts$)$You can't register for CS$3343$ only if you haven't passed both CS$2233$ and CS$3333.$

$(3)(10$ pts$)$If you can register for CS$3343$ then you have passed CS$2233$ and you understand boolean algerbra if you passed CS$2233.$

$2.$ Equivalences