<div><strong>Discrete Structures Prefinal - Logic</strong></div> | Take the Quiz

A vibrant and engaging image depicting a student studying discrete mathematics, surrounded by logic symbols and truth tables, with a chalkboard in the background.

Discrete Structures Logic Quiz

Test your understanding of discrete structures and logic with our engaging prefinal quiz! Designed to challenge students, this quiz covers various essential concepts in logic and propositional calculus.

Key features:

Comprehensive questions on truth tables, logical equivalences, and statement forms.
Multiple choice, drop-down, and text entry formats to enhance engagement.
Perfect for students preparing for exams in discrete mathematics.

82 Questions20 MinutesCreated by AnalyzingLogic42

Read each item carefully and select the best answer/s or encode your answer as directed.
Answers in short-response questions are not case-sensitive BUT are space sensitive - DO NOT put any space between symbols, numbers, and letters within an expression - e.g. "1,2,3" "p∧(q∨r)→s" NOT "1, 2, 3" "p ∧ (q ∨ r) → s"
NO CHEATING - Opening of other tabs and using of any computing devices during the test are not allowed.
Backtracking is DISABLED in this quiz - make sure you place a response and review before proceeding to the next item.

Read each item carefully and select the best answer/s or encode your answer as directed.
Answers in short-response questions are not case-sensitive BUT are space sensitive - DO NOT put any space between symbols, numbers, and letters within an expression - e.g. "1,2,3" "p∧(q∨r)→s" NOT "1, 2, 3" "p ∧ (q ∨ r) → s"
NO CHEATING - Opening of other tabs and using of any computing devices during the test are not allowed.
Backtracking is DISABLED in this quiz - make sure you place a response and review before proceeding to the next item.

Complete the truth table below. (6 points)

	P ∧ Q	P ∨ Q	P ∧ Q → P ∨ Q
P: T and Q: T
P: T and Q: F
P: F and Q: T
P: F and Q: F

A statement that is always true in every possible interpretation. (2 points)

Define a knight as someone telling the truth and a knave as someone telling a lie.

Suppose you meet two persons X and Y and they said the following:

X: Y and I are of opposite type.

Y: X is a knight.

Who are X and Y? (4 points)


X is a:
Y is a:

Which of the following are statements? Choose all that apply. (3 points)

2 + 2 > 5

She is a high school student.

X^2 + y^2 = 1

Jim is tall but he is heavy.

Which of the following is considered ambiguous? (2 points)

~ (~a ∧ b)

A ∧ b ∨ c

A ∧ b ∧ c ∧ d → e

None of the choices

Let c = "It is cold", s = "It is windy". Translate "It is neither cold nor windy" into symbols. (no spacing, copy-paste the ff. symbols: ~ ∧ ∨ → ) (3 points)

Suppose x is a particular real number. Let p = "0 < x", q = "x < 10", r = "x = 10". Choose the correct statement below that represents: (3 points)

	P ∧ q	(q ∨ r) ∧ p	P ∧ (q ∧ r)	P ∨ (q ∨ r)
0 < x < 10
0 < x ≤ 10

Construct a truth table for (p ∧ q) ∨ ~r.

Question: How many "T"s are there in the last column " (p ∧ q) ∨ ~r "?

(4 points)

Which of the following is equivalent to the statement ~(p ∧ q) ? (2 points)

~p ∧ ~q

~p ∨ ~q

~p ∧ q

~p ∨ q

Which of the following negates " -3 < x ≤ 7" ? (2 points)

-3 ≥ x and x > 7

-3 ≥ x or x > 7

-3 > x or x ≥ 7

-3 ≥ x > 7

It is a statement form that is always false regardless of the truth values of the individual statements substituted for its statement variable. (2 points)

Which of the following is TRUE? (Let t be a tautology and c be a contradiction) (2 points)

P ∨ ~p is always true.

P ∧ t is always false.

P ∧ t is always true.

P ∧ c is sometimes false.

Identify the laws demonstrated by statements 2, 4, 7, 8, and 10. (5 points)

	Laws
Statement 2
Statement 4
Statement 7
Statement 8
Statement 10

Use a truth table to evaluate (p ∧ q) ∨ (~p ∨ (p ∧ ~q)). Choose the correct answer below. (5 points)

Tautology

Contradiction

Contingency (neither tautology nor contradiction)

It is the science of reasoning, whose purpose is mainly to make valid arguments. (1 point)

A declarative sentence or series of declarative statements that has either a truth value of true or false but not both. (1 point)

Logic

Argument

Proposition

Conclusion

The preceding statements in an argument prior to the conclusion are called: (1 point)

Given a statement p → q which is true. Which among the following are TRUE? (Choose all that apply) (3 points)

Its converse is always true.

Its inverse is not always true.

Its contrapositive is always true.

Its biconditional is not always true.

The negation of p → q is: (2 points)

~p → ~q

P ∧ ~q

~p ∧ q

P ∨ ~q

Evaluate p ∨ ~q → ~p when p is TRUE and q is TRUE. (3 points)

True

False

True or False: ~p ∨ q is equivalent to p → q. (2 points)

True

False

Rewrite the following statement without using "if" and "then": If you do not get to class on time, then you are suspended" (3 points)

Either you get to class on time or you are suspended.

Either you do not get to class on time or you are suspended.

You do not get to class and you are suspended.

You get to class and you are not suspended.

Negate the statement "If May lives in Manila, then she lives in Luzon" (3 points)

May does not live in Manila but lives in Luzon.

May lives in Manila but does not live in Luzon.

May lives in neither Manila nor Luzon.

Either May lives in Manila or she lives in Luzon.

If the statement "If today is November 8, then tomorrow is not Sunday." is true, which of the following are FALSE? Choose all that apply. (5 points)

If tomorrow is Sunday, then today is not November 8.

If today is not November 8, then tomorrow is Sunday.

If tomorrow is not Sunday, then today is November 8.

Today is not November 8 and tomorrow is not Sunday.

True or False: The statement p ↔ q is equivalent to (p → q) ∧ (q → p). (3 points)

True

False

True or False: In logic, a hypothesis and conclusion are required to have related subject matters. (2 points)

True

False

Determine whether the following are logically equivalent:

I. If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n

II. 2 is not a factor of n or 3 is not a factor of n and 6 is not a factor of n

(4 points)

I and II are logically equivalent

I and II are not logically equivalent.

True or False: In informal language, simple conditional statements are often used to mean biconditionals.

(1 point)

True

False

Refer to the picture above. Which of the following could be in the "?" cell? (Choose all that apply) (3 points)

~(~(~p)))

P ∧ T

P ∧ p

Which of the following statements is NOT logically equivalent to "p"?

(3 points)

P ∧ p

P ∧ t (tautology)

~(~p))

P ∧ c (contradiction)

Simplify the expression ~(~p ∧ q) ∧ (p ∨ q).

HINT: The following laws are involved in order: De Morgan's laws, Double negation law, distributive law, Commutative law, Negation law, Identity Law

(4 points)

True or False: P and Q are logically equivalent if P ↔ Q is a tautology. (2 points)

True

False

Determine the truth value of the conjunction of the statements below given:

P is the proposition 12 is divisible by 3

Q is the proposition 3 is a prime number

(3 points)

True

False

True or False: Given the statement Q implies P, the conditional statement is false when P is true and Q is false, and true otherwise. (2 points)

True

False

Refer to the picture above. Identify the rule of inference exemplified by arguments 1, 4, 5, 6, and 8. (5 points)


Argument 1
Argument 4
Argument 5
Argument 6
Argument 8

True or False: To say an argument form is valid means that no matter what particular statements are substituted for the statement variables in its premises, if the resulting premises are all true, then the conclusion is also true. (2 points)

True

False

Construct a truth table to check the validity of the following argument form:

P → q ∨ ~r

q → p ∧ r

Therefore, p → r

Which statements below are TRUE? (Choose all that apply) (5 points)

There are four critical rows.

All critical rows lead to true conclusions.

There are five critical rows.

Not all critical rows lead to true conclusions.

The argument form is valid.

The argument form is invalid.

Which of the following is false? (2 points)

A syllogism is an argument form consisting of at least two premises and a conclusion.

The first premise is called a major premise.

The last premise is called a minor premise.

None of the choices.

Identify the rule of inference in this example:

x + 2 = 0 or x - 5 = 0; x is nonnegative; therefore, x = 5. (2 points)

Specialization

Conjunction

Elimination

Modus Ponens

It is an error in reasoning that results in invalid arguments. (2 points)

An inverse error is committed through the fallacy of: (2 points)

Affirming the consequence

Affirming the antecedent

Denying the consequence

Denying the antecedent

An argument is called ____ if and only if it is valid and all its premises are true. (2 points)

True or False: If one can show that the supposition which statement p is false leads logically to a contradiction, then he or she can deduce that p is false. (2 points)

True

False

The argument form "If this number is larger than 2, then its square is larger than 4. This number is not larger than 2. Therefore, the square of this number is not larger than 4" is: (3 points)

Valid via Modus Ponens

Valid via Modus Tollens

Valid via Contradiction Rule

Invalid

True or False: We can only be sure that the conclusion of an argument is true when we know the argument is valid. (2 points)

True

False

You are about to leave for school in the morning and discover that
you don't have your glasses. You know the following statements
are true:

If I was reading a newspaper in the kitchen, then my glasses are on the kitchen table.
If my glasses are on the kitchen table, then I saw them at breakfast.
I did not see my glasses at breakfast.
I was reading the news paper in the living room or I was reading the newspaper in the kitchen.
If I was reading the news paper in the living room then my glasses are on the coffee table.

Arragnge the following premises and conclusions in the order they are derived. (Not all are necessarily used)

I was not reading the newspaper in the kitchen.
If I did not see my glasses at breakfast, then I was reading the newspaper in the living room.
My glasses are on the coffee table.
My glasses are on the kitchen table.
I was reading the newspaper in the living room.
I saw my glasses at breakfast.
If I was reading the newspaper in the kitchen, then I saw my glasses at breakfast.

(6 points)

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Derived Premise 1
Derived Premise 2
Derived Premise 3
Conclusion

Which among the following symbols is evaluated last? (1 point)

�

Unlock and Upgrade

Remove all limits from your Quizzes

Discrete Structures Prefinal - Logic

Discrete Structures Logic Quiz

More Quizzes