Question

1. Translate the following English expressions into logical statements. You must explicitly state what the atomic propositions are (e.g., "Let p be proposition ...") and then show their logical relation.

a. If it is red then it is not blue and it is not green.

b. It is white but it is also red and green and blue.

c. It is black if and only if it is not red, green, or blue.

2. Determine if the following expressions are tautologies, contradictions, or contingencies by using only truth tables. Show all your work and do not skip any steps (i.e., ensure you that you include a new column for every single operation, and that you state at the endwhether each expression is a tautology, contingency, or contradiction).

a. ¬ (? ∧ (¬? ∨ (? → ?)))

b. (? ∨ (? ↔ (¬? ∧ (? ∨ ?))))

c. (? ∧ ¬ (? ∧ (? ∨ (? ↔ ?))))

d. ¬ (? ∨ ¬(? → (? ∧ ?)))

Answer 1