Logical equivalence
a) Use a truth table to demonstrate that p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r).
b) Use a truth table to demonstrate that p ∧ q ≡ ¬(¬p ∨ ¬q).
c) Use substitutions and the transitive property of logical equivalence to show that
p → q ≡ ¬(p ∧ ¬q).
Provide a justification for each step (i.e. substitution or transitivity, and what logical equivalences you are using.)
d) Use substitutions and the transitive property of logical equivalence to show that
p ↔ q ≡ (¬p ∨ q) ∧ (¬q ∨ p).
Provide a justification for each step (i.e. substitution or transitivity, and what logical equivalences you are using.)