# Edit this file to list your answers to the Propositional Completeness
# problem.
#
# You can enter your formulas here in any format that our Truth Table Tool
# (web.stanford.edu/tools/truth-table-tool/) can understand. For example,
# all of the following are ways of saying "p ∧ q → ¬r":
#
#     p ∧ q → ¬r
#     p and q implies not r
#     p && q => !r
#     p /\ q -> ~r
#     p \land q \to \neg r
#
# As a note, variables are case-sensitive, so p and P are not treated as
# the same variable.
#
# You can represent the ⊤ and ⊥ connectives either by using those symbols
# directly, by writing out true or false, etc.
#
# All blank lines are ignored, as is any text after a hash mark (#).
# Feel free to introduce whatever whitespace you'd like to have in your
# formulas. That will make things easier to read and edit if you need to
# read or edit them. :-)

[Part (i)]   # Express ⊥; don't use connectives other than ∧, ∨, ¬, and ⊤









[Part (ii)]  # Express p → q; don't use connectives other than ∧, ∨, ¬, and ⊤









[Part (iii)] # Express p ↔ q; don't use connectives other than ∧, ∨, ¬, and ⊤









[Part (iv)]  # Express p ∨ q; don't use connectives other than ∧, ¬, and ⊤









[Part (v)]   # Express ⊤; don't use connectives other than → and ⊥









[Part (vi)]  # Express ¬p; don't use connectives other than → and ⊥









[Part (vii)] # Express p ∧ q; don't use connectives other than → and ⊥









