COT FINAL EXAM QUESTIONS AND
ANSWERS. VERIFIED 2026.
Which of the following sentences are propositions? Select all that apply.
On your mark, get set, go.
(1+2+3)/2 = 3
sin(π) + cos(π) < 0.5
Be quiet! - ANS (1+2+3)/2 = 3
sin(π) + cos(π) < 0.5
Let p and q be propositional variables. Which of the following expressions are NOT well-defined
formulas of propositional logic? Select all that apply.
¬
T→q
¬(((p ∧ q) ∧ ¬q) ∧ p)
∀p∀q(p v q) - ANS ∀p∀q(p v q)
¬
Consider the propositions
p: lunch includes rice
q: lunch includes pasta.
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, Translate the following expressions of the natural language into formulas: - ANS lunch
includes either rice or pasta. p v q
lunch includes neither rice nor pasta. ¬p ∧ ¬q
lunch includes rice but not pasta p ∧ ¬q
lunch includes rice and pasta. p ∧ q
Determine whether the given conditional statements are T (true) or F (false).
(a) If 2 + 2 = 5 then 2/0 = 2
(b) If 2 +2 = 5 then 4 is an even number
(a) If the Earth is flat then -1 + 1 = 0 T
(b) If 1 < 0 then UFOs exist T - ANS T, T
T,T
The order of operations in the formula p ∨ q ∧ r → q is the same as in ____.
The order of operations in the formula p → r ∨ ¬p ↔ r is the same as in ____. - ANS ((p ∨ q)
∧ r) → q
(p → (r ∨ (¬p))) ↔ r
Consider the formula
((p → q) ∧ p) → q
(a) Complete the truth table below, writing the capital letters T or F in the given spaces.
(Remember that in our course we use T/F to denote the truth values, so don't enter other forms
such as 1/0, true/false, t/f, etc.)
(b) Is the formula valid, satisfiable (but not valid), or unsatisfiable (write down in the given space
valid, satisfiable, or unsatisfiable)? - ANS T, T, T, T, VALID
The number of interpretations of a formula with 8 propositional variables is ___.
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
ANSWERS. VERIFIED 2026.
Which of the following sentences are propositions? Select all that apply.
On your mark, get set, go.
(1+2+3)/2 = 3
sin(π) + cos(π) < 0.5
Be quiet! - ANS (1+2+3)/2 = 3
sin(π) + cos(π) < 0.5
Let p and q be propositional variables. Which of the following expressions are NOT well-defined
formulas of propositional logic? Select all that apply.
¬
T→q
¬(((p ∧ q) ∧ ¬q) ∧ p)
∀p∀q(p v q) - ANS ∀p∀q(p v q)
¬
Consider the propositions
p: lunch includes rice
q: lunch includes pasta.
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, Translate the following expressions of the natural language into formulas: - ANS lunch
includes either rice or pasta. p v q
lunch includes neither rice nor pasta. ¬p ∧ ¬q
lunch includes rice but not pasta p ∧ ¬q
lunch includes rice and pasta. p ∧ q
Determine whether the given conditional statements are T (true) or F (false).
(a) If 2 + 2 = 5 then 2/0 = 2
(b) If 2 +2 = 5 then 4 is an even number
(a) If the Earth is flat then -1 + 1 = 0 T
(b) If 1 < 0 then UFOs exist T - ANS T, T
T,T
The order of operations in the formula p ∨ q ∧ r → q is the same as in ____.
The order of operations in the formula p → r ∨ ¬p ↔ r is the same as in ____. - ANS ((p ∨ q)
∧ r) → q
(p → (r ∨ (¬p))) ↔ r
Consider the formula
((p → q) ∧ p) → q
(a) Complete the truth table below, writing the capital letters T or F in the given spaces.
(Remember that in our course we use T/F to denote the truth values, so don't enter other forms
such as 1/0, true/false, t/f, etc.)
(b) Is the formula valid, satisfiable (but not valid), or unsatisfiable (write down in the given space
valid, satisfiable, or unsatisfiable)? - ANS T, T, T, T, VALID
The number of interpretations of a formula with 8 propositional variables is ___.
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
