- 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:
- If it is not raining, I will go outside.
- It is raining and I will bring an umbrella or I will get wet.
- If it is raining, I will go outside and if I bring an umbrella, I will not get wet.
- If and only if it is raining, I will get wet if I go outside and do not bring an umbrella
- Show that the following pairs of statements are equal to each other using truth tables.
- p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)
- p → q = ~q → ~p
- 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.