MAT 243 Final Exam Review Questions
and Answers
Consider the statement "Unless you stop smoking, you will get sick". Select which one of the following
statements are logically equivalent to that conditional above. - Answer-You will get sick if you keep
smoking.
Continuing to smoke is sufficient to get sick.
How many distinct ternary logical operators are there? A ternary logical operator is an operator that
takes three inputs, p, q and r, and for each truth configuration of the inputs, outputs true or false.
Recall that a logical operator is defined by its truth table. - Answer-256
Select which one of the following statements is logically equivalent to (p∨q) → r . - Answer-( p→ r ) ∧
( q→ r )
Evaluate 1010 OR 0011. Here, OR is the bitwise logical or, acting on bitstrings. - Answer-1011
Match logically equivalent expressions.
p ↔ q - Answer-¬ ((p ∨ q) ∧¬ (p ∧ q)).
Match logically equivalent expressions.
p ⊕ q - Answer-(p ∨ q) ∧¬ (p ∧ q).
, Match logically equivalent expressions.
p ∨ q - Answer-¬p → q
Match logically equivalent expressions.
p ∧ q - Answer-¬(¬p ∨¬ q).
Determine the truth of the quantified statement
∀x ∃y (xy > x).
The domain of discourse is the set of real numbers. - Answer-False
Determine the truth of the quantified statement
∀x ∃y (xy > x).
The domain of discourse is the set of positive real numbers. - Answer-True
Enter the smallest integer n so that the following function is O(xⁿ).
f(x)=x²(x³ + 1)+x⁵log(x). - Answer-6
Check all functions f(x) that are O(x²). - Answer-f(x) = log(xˣ)
f(x) = ⌊x+2⌋ · ⌈x⌉
f(x)=2x^1.9 +2x^-1.9
f(x) = (x⁴+2x+3)/(x²-2)
Given an increasing big-O order of the functions. This means that f1 is O(f2), f2 is O(f3), etc. - Answer-
log(n)
n
nlog(n)
and Answers
Consider the statement "Unless you stop smoking, you will get sick". Select which one of the following
statements are logically equivalent to that conditional above. - Answer-You will get sick if you keep
smoking.
Continuing to smoke is sufficient to get sick.
How many distinct ternary logical operators are there? A ternary logical operator is an operator that
takes three inputs, p, q and r, and for each truth configuration of the inputs, outputs true or false.
Recall that a logical operator is defined by its truth table. - Answer-256
Select which one of the following statements is logically equivalent to (p∨q) → r . - Answer-( p→ r ) ∧
( q→ r )
Evaluate 1010 OR 0011. Here, OR is the bitwise logical or, acting on bitstrings. - Answer-1011
Match logically equivalent expressions.
p ↔ q - Answer-¬ ((p ∨ q) ∧¬ (p ∧ q)).
Match logically equivalent expressions.
p ⊕ q - Answer-(p ∨ q) ∧¬ (p ∧ q).
, Match logically equivalent expressions.
p ∨ q - Answer-¬p → q
Match logically equivalent expressions.
p ∧ q - Answer-¬(¬p ∨¬ q).
Determine the truth of the quantified statement
∀x ∃y (xy > x).
The domain of discourse is the set of real numbers. - Answer-False
Determine the truth of the quantified statement
∀x ∃y (xy > x).
The domain of discourse is the set of positive real numbers. - Answer-True
Enter the smallest integer n so that the following function is O(xⁿ).
f(x)=x²(x³ + 1)+x⁵log(x). - Answer-6
Check all functions f(x) that are O(x²). - Answer-f(x) = log(xˣ)
f(x) = ⌊x+2⌋ · ⌈x⌉
f(x)=2x^1.9 +2x^-1.9
f(x) = (x⁴+2x+3)/(x²-2)
Given an increasing big-O order of the functions. This means that f1 is O(f2), f2 is O(f3), etc. - Answer-
log(n)
n
nlog(n)
