Problem 1 (10 points)

Problem 1a (3 points): Write the following sentence using propositional calculus. Identify and write the propositions clearly. (0.5 point for identifying each proposition + 1.5 points for the compound proposition). There are three propositions.

"COVID-19 virus can be cured only if people are disciplined and vaccine works"

Problem 1b (2 points) Write an optimized sentence and explain the rationale.

Let p, q, r be thepropositions.

p : I have taken vaccine q : I use face mask r: I will not get COVID19

(p q) r

Problem 1c. (5 points) write the compound proposition in 1b in Conjunctive normal form by applying implication transformation, De Morgans law and distributive law, then make a truth table for the resulting compound proposition (2 points for De Morgans law application + 3 points for the truth table)

(p q) r