1.1 Propositional Logic

• Proposition - A statement that has a truth value.
• Truth table and how to construct one.
• Logical operations - and ($\land$), or ($\lor$), negation ($\neg$).
• Implication (If assumption is false, the conclusion is always true).

  $p\to q$, if $p$, then $q$.
  If $p$ (assumption) is false, $p\to q$ (conclusion) is always true.

• Bi-implication (Double implication, if and only if) $p \iff q \equiv (p \to q \land q \to p)$.
• Contrapositive - The contrapositive of $p\to q \text{ is } \lnot q \to \lnot p$.

Homework

p34: 31d, 32de, 38, 39

31. Construct a truth table for each of these compound propositions.
d). $(p \lor q) \to (p \land q)$

32. Construct a truth table for each of these compound propositions.
d. $(p \land q) \to (p \lor q)$

e. $(q \to \neg p) \bi (p \bi q)$

38. Construct a truth table for $((p \to q) \to r) \to s$.

39. Construct a truth table for $(p \bi q) \bi (r \bi s)$.