Propositional Statements And Logical Relationships Quiz

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1) The statement “If it rains, then I take an umbrella” is:

Conjunction

Disjunction

Conditional (implication)

Biconditional

This is an "if-then" statement, which in logic is represented by implication (→).

Explanation

This is an "if-then" statement, which in logic is represented by implication (→).

About This Quiz

Propositional Statements and Logical Relationships Quiz - Quiz

Are you ready to see how logic helps us analyze everyday claims? This quiz dives into propositions, implications, biconditionals, and exclusive OR statements. You’ll practice identifying which sentences count as propositions, evaluating compound statements, and applying core rules like the law of excluded middle. With each question, you’ll discover how... see moretruth values behave, how statements relate to one another, and how logic turns ordinary language into clear, testable expressions. By the end, you’ll have a solid foundation in understanding the structure of logical reasoning!
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2) Which statement matches P∧Q?

P or Q

P and Q

If P then Q

Not P or Q

The symbol ∧ represents logical conjunction or "and".

Explanation

The symbol ∧ represents logical conjunction or "and".

3) The truth value of P↔Q is true when:

Both are false

At least one is true

They have the same truth value

Both are true

Biconditional (↔) is true when both statements are simultaneously true or simultaneously false.

Explanation

Biconditional (↔) is true when both statements are simultaneously true or simultaneously false.

4) “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 describes a biconditional relationship between studying and passing. From “If I study, I pass” (S → P) and “If I don’t study, I fail” (¬S → ¬P), the second is equivalent to P → S (contrapositive). So we have S → P and P → S, i.e., S ↔ P.

Explanation

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

True

False

Neither

This is the law of excluded middle in classical logic.

Explanation

This is the law of excluded middle in classical logic.

6) The statement “7 is odd OR 10 is even” is:

True

False

Neither

Since 10 is even, the entire disjunction is true regardless of whether 7 is odd.

Explanation

Since 10 is even, the entire disjunction is true regardless of whether 7 is odd.

7) Which is NOT a binary connective?

∧

∨

→

Negation (¬) is a unary operator as it acts on only one operand.

Explanation

Negation (¬) is a unary operator as it acts on only one operand.

8) Evaluate: P ∧ Q where P = T and Q = F.

True

False

Undefined

Depends on context

Conjunction (AND) is only true when both operands are true.

Explanation

Conjunction (AND) is only true when both operands are true.

9) Wvaluate: (P → Q) ∧ (Q → P) where P = T and Q = F.

True

False

Undefined

Tautology

This is logically equivalent to P ↔ Q. When P and Q have different truth values, the biconditional is false. Thus the entire expression evaluates to False.

Explanation

This is logically equivalent to P ↔ Q. When P and Q have different truth values, the biconditional is false. Thus the entire expression evaluates to False.

10) 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

An implication is only false when the premise (P) is true but the conclusion (Q) is false.

Explanation

An implication is only false when the premise (P) is true but the conclusion (Q) is false.

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

True

False

Unknown

Contradiction

Disjunction (OR) is true when at least one operand is true.

Explanation

Disjunction (OR) is true when at least one operand is true.

12) The implication “If 3333 is smaller than 10 then it is smaller than 5” is:

Cannot be determined

False

True

An implication with a false premise is always true in logic.

Explanation

An implication with a false premise is always true in logic.

13) From P ∧ Q, what can we validly conclude?

P only

Q only

Either P or Q

Both P and Q

If P ∧ Q is true, then both P and Q must be true individually.

Explanation

If P ∧ Q is true, then both P and Q must be true individually.

14) In propositional logic, the XOR (exclusive OR) connective yields a true result in which of the following cases?

Both are true

Exactly one is true

At least one is true

Both are false

XOR is true when the operands have different truth values - one true and one false. It is false when both statements share the same truth value, whether both are true or both are false. That’s why it’s called an exclusive OR. In contrast, the AND connective is true only when both are true, and the inclusi ⅴ e OR is true when at least one is true.

Explanation

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Alva Benedict B. |PhD

College Expert

Alva Benedict B. is an experienced mathematician and math content developer with over 15 years of teaching and tutoring experience across high school, undergraduate, and test prep levels. He specializes in Algebra, Calculus, and Statistics, and holds advanced academic training in Mathematics with extensive expertise in LaTeX-based math content development.