Homework 2
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.
. Write your 3 compound statements symbolically.
c. Write truth tables for your three compound statements.
2) Construct a truth table for the following statements:
a. ~q → p
. (p ∧ q) → (q ∧ p)
c. 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
ing an um
ella” and s be “I will get wet”.
Translate the following sentences into symbolic logic:
a. If it is not raining, I will go outside.
. It is raining and I will
ing an um
ella or I will get wet.
c. If it is raining, I will go outside and if I
ing an um
ella, I will not get wet.
d. If and only if it is raining, I will get wet if I go outside and do not
ing an um
ella
5) Show that the following pairs of statements are equal to each other using truth tables.
a. p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)
. 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.