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...

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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. b. 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 b. (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 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.