# Write 2 simple statements and 3 compound statements in sentence form. For the compound statements, use a different connective for each.

1. a. Write 2 simple statements and 3 compound statements in sentence form.  For the compound statements, use a different connective for each.  You need to have a negation in at least one of your compound statements.  Underline the connectives.

b. Write your 3 compound statements symbolically.

c. Write truth tables for your three compound statements.

•  Construct a truth table for the following statements:
•  ~q → p
• (p ∧ q) → (q ∧ p)
• r ↔ (p ∨ ~q)
•  How many lines would a truth table for the following statement contain?  For bonus points, construct the truth table.

(~p ∧ ~q) → (s → r)

• Let p be “it is raining”, q be “I will go outside”, r be “I will bring an umbrella” and s be “I will get wet”.

Translate the following sentences into symbolic logic:

1.  If it is not raining, I will go outside.
2. It is raining and I will bring an umbrella or I will get wet.
3. If it is raining, I will go outside and if I bring an umbrella, I will not get wet.
4. If and only if it is raining, I will get wet if I go outside and do not bring an umbrella
5. Show that the following pairs of statements are equal to each other using truth tables.
6. p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)
7. p → q = ~q → ~p
8. Bonus:  Create 4 statements in the mold of the statements in number 4.  The statements should be at least somewhat related.  Write 4 sentences using these statements, translate these sentences into symbolic logic and write truth tables for the four.