Propositional Logic and Operators

Fun class activity:

1. Represent the following compound propositions using logical operators. You can use the variables $p, q,$ and $r$ to represent simple statements inside those propositions:
   1. The integer $3$ is even, and $2-1=1$.
   2. The integer $9$ is divisible by $3$, or the integer $9$ is not divisible by $3$.
   3. If Earth is flat, then today is a Monday or Wednesday.
   4. The integer $n$ is equal to $2$ if and only if the integer $n$ is bigger than $1$ and the integer $n$ is smaller than $3$.
2. For each of the compound propositions above, indicate if it is true or false. Explain your answer.

Precedence of operations: Parentheses () are evaluated before negation ($\neg$); negation before conjunction ($\wedge$); conjunction before exclusive disjunction ($\oplus$); exclusive disjunction before disjunction ($\vee$); disjunction before implications ($\rightarrow$); and implications before biconditionals ($\leftrightarrow$).