Propositional Logic Quiz � Reason Abstractly & Critique Logical Arguments (MP.2, MP.3)

1) Every proposition must be either true or false, not both.

True

False

This is the law of the excluded middle.

Explanation

This is the law of the excluded middle.

2) ‘If I study, I pass. If I don’t study, I fail.’ concludes:

No conclusion

I pass if and only if I study

Studying is unnecessary

Both outcomes true

This is a biconditional: outcome tied to studying.

Explanation

This is a biconditional: outcome tied to studying.

3) Which pair is logically equivalent?

P→QP \to QP→Q and ¬P∨Q\neg P \lor Q¬P∨Q

P→QP \to QP→Q and P∧QP \land QP∧Q

P→QP \to QP→Q and Q→PQ \to PQ→P

P→QP \to QP→Q and P∨QP \lor QP∨Q

Implication rewrites as ¬P∨Q\neg P \lor Q¬P∨Q.

Explanation

Implication rewrites as ¬P∨Q\neg P \lor Q¬P∨Q.

4) Simplify ¬(P∨Q)\neg(P \lor Q)¬(P∨Q).

¬P∧¬Q\neg P \land \neg Q¬P∧¬Q

¬P∨¬Q\neg P \lor \neg Q¬P∨¬Q

P∧QP \land QP∧Q

P∨QP \lor QP∨Q

By De Morgan’s Law, NOT(OR) = AND of negations.

Explanation

By De Morgan’s Law, NOT(OR) = AND of negations.

5) The biconditional 'P ↔ Q' is true when:

Both are true

Both are false

They have the same truth value

At least one is true

Biconditional means equivalence of truth values.

Explanation

Biconditional means equivalence of truth values.

6) ‘If it rains, the street is wet. The street is wet, so it rained.’ is which fallacy?

Affirming the consequent

Denying the antecedent

Modus ponens

Modus tollens

Wet street doesn’t imply only rain could cause it.

Explanation

Wet street doesn’t imply only rain could cause it.

7) The statement 'If it rains, then I will take an umbrella' is:

Conjunction

Disjunction

Conditional (implication)

Biconditional

This is an implication (P → Q).

Explanation

This is an implication (P → Q).

8) If P is true and Q is false, then P ∨ Q is:

True

False

Unknown

Contradiction

OR is true if at least one part is true.

Explanation

OR is true if at least one part is true.

9) Which of the following is a proposition?

Open the book.

The Earth revolves around the Sun.

Are you ready?

Please be quiet!

A proposition is a declarative sentence that can be true or false.

Explanation

A proposition is a declarative sentence that can be true or false.

10) ‘All humans are mortal. Socrates is a human. Therefore Socrates is mortal.’ This is:

Invalid reasoning

A fallacy

A valid deductive argument

An analogy

This is a valid syllogism.

Explanation

This is a valid syllogism.

11) Which of these is a tautology?

P ∨ ¬P

P ∧ ¬P

P → Q

¬P → P

‘P or not P’ is always true.

Explanation

‘P or not P’ is always true.

12) An implication 'If P then Q' is false only when:

P is false and Q is false

P is true and Q is false

P is false and Q is true

Both are true

Implication is false only when a true premise leads to a false conclusion.

Explanation

Implication is false only when a true premise leads to a false conclusion.

13) Which statement matches P ∧ Q?

P or Q

P and Q

If P then Q

Not P or Q

Conjunction requires both parts to be true.

Explanation

Conjunction requires both parts to be true.

14) The statement '7 is odd OR 10 is even' is true.

True

False

A disjunction is true if at least one part is true.

Explanation

A disjunction is true if at least one part is true.

15) Which is a contradiction?

P∨QP \lor QP∨Q

P∧¬PP \land \neg PP∧¬P

P→QP \to QP→Q

P↔QP \leftrightarrow QP↔Q

‘P and not P’ is always false.

Explanation

‘P and not P’ is always false.

16) ‘If P then Q. Q. Therefore P.’ is:

Valid

Modus ponens

Modus tollens

Invalid (fallacy)

This is the fallacy of affirming the consequent.

Explanation

This is the fallacy of affirming the consequent.

17) The implication 'If the sky is green, then 2+2=5' is true.

True

False

A false premise makes the implication true regardless of conclusion.

Explanation

A false premise makes the implication true regardless of conclusion.

18) The contrapositive of 'If P then Q' is:

If Q then P

If not P then not Q

If not Q then not P

If P then not Q

Contrapositive: “If ¬Q then ¬P”, always equivalent to the original.

Explanation

Contrapositive: “If ¬Q then ¬P”, always equivalent to the original.

19) The negation of 'All birds can fly' is:

No birds can fly

Some birds cannot fly

Birds can swim

Birds are mammals

The negation of 'All' is 'Some…not'.

Explanation

The negation of 'All' is 'Some…not'.

20) From (P∧Q)(P \land Q)(P∧Q), what can we validly conclude?

P only

Q only

Either P or Q

Both P and Q

Conjunction allows us to infer both P and Q separately.

Explanation

Conjunction allows us to infer both P and Q separately.

Understanding and Evaluating Logical Statements

1) Every proposition must be either true or false, not both.

2)

What first name or nickname would you like us to use?

2) ‘If I study, I pass. If I don’t study, I fail.’ concludes:

3) Which pair is logically equivalent?

4) Simplify ¬(P∨Q)\neg(P \lor Q)¬(P∨Q).

5) The biconditional 'P ↔ Q' is true when:

6) ‘If it rains, the street is wet. The street is wet, so it rained.’ is which fallacy?

7) The statement 'If it rains, then I will take an umbrella' is:

8) If P is true and Q is false, then P ∨ Q is:

9) Which of the following is a proposition?

10) ‘All humans are mortal. Socrates is a human. Therefore Socrates is mortal.’ This is:

11) Which of these is a tautology?

12) An implication 'If P then Q' is false only when:

13) Which statement matches P ∧ Q?

14) The statement '7 is odd OR 10 is even' is true.

15) Which is a contradiction?

16) ‘If P then Q. Q. Therefore P.’ is:

17) The implication 'If the sky is green, then 2+2=5' is true.

18) The contrapositive of 'If P then Q' is:

19) The negation of 'All birds can fly' is:

20) From (P∧Q)(P \land Q)(P∧Q), what can we validly conclude?