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

Truth table exercise answers

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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