# 8.2.2 Truth table exercises

8.2.2

I.   Truth table exercise

Work with a partner to put these pairs of statements into symbols; then build the truth-tables for them to determine both what kind of statement each is and how each relates to the one it is paired with.   Answers below.

1. Either p or q                                                If not p, then q

2. Either both p and q or else neither              p implies q and q implies p

3. Neither p nor q                                            Not p and not q

4. Either not p or else not q                             Not both p and q

5. p implies q                                                   Not q implies not p

6. Either p or else q and r                                Either p or q and either p or r

Put these pairs of statements into symbols, then build the truth-tables for them to determine both what kind of statement each is and how each relates to the one it is paired with.

1. Either p or q            p v q                            If not p, then q     ~p > q

Both contingent; equivalent pair

2. Either both p and q or else neither              p implies q and q implies p

(p . q) v ~(p v q)                                              (p > q) . (q > p)

Both contingent; equivalent pair

3. Neither p nor q        ~(p v q)                       Not p and not q      ~ p . ~q

Both contingent; equivalent pair

4. Either not p or else not q     ~p v ~q                        Not both p and q   ~(p . q)

Both contingent; equivalent pair

5. p implies q        p > q                                      Not q implies not p    ~q > ~p

Both contingent; equivalent pair

6. Either p or else q and r                                Either p or q and either p or r

p v (q . r)                                                         (p v q) . (p v r)

both contingent; equivalent pair

II.

1 Fill in the values under the main operators to determine which of these are equivalent to others.

~(p . q)             ~p v ~q             ~(p v q)               ~p . ~q                 p > ~q

2 What do the tables tell you about these?

p > q                  q > p                    ~(~p v q)                ~q > ~p                         p . ~p

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