Assignment

1a) 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:

i) ~q → p

ii) (p ∧ q) → (q ∧ p)

iii) r ↔ (p ∨ ~q)

3)How many lines would a truth table for the following statement contain? For bonus points, construct the truth table.

(~p ∧ ~q) → (s → r)

4)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:

a) If it is not raining, I will go outside.

b)It is raining and I will bring an umbrella or I will get wet.

c)If it is raining, I will go outside and if I bring an umbrella, I will not get wet.

d)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.

a) p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)

b)p → q = ~q → ~p

6) 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.