Propositional Statements and Logical Relationships Quiz

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| Questions: 14 | Updated: Dec 1, 2025
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1) The statement “If it rains, then I take an umbrella” is:

Explanation

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

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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! see less

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2) Which statement matches P∧Q?

Explanation

The symbol ∧ represents logical conjunction or "and".

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3) An implication “If P then Q” is false only when:

Explanation

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

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

Explanation

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

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5) “If I study, I pass. If I don’t study, I fail.” concludes:

Explanation

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.

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

Explanation

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

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

Explanation

This is the law of excluded middle in classical logic.

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

Explanation

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

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

Explanation

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

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

Explanation

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

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11) Which is NOT a binary connective?

Explanation

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

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

Explanation

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

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

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.

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

Explanation

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.

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The statement “If it rains, then I take an umbrella” is:
Which statement matches P∧Q?
An implication “If P then Q” is false only when:
The truth value of P↔Q is true when:
“If I study, I pass. If I don’t study, I fail.” concludes:
If P is true and Q is false, then P∨Q is:
Every proposition must be either true or false, not both.
The statement “7 is odd OR 10 is even” is:
The implication “If 3333 is smaller than 10 then it is smaller than...
From P ∧ Q, what can we validly conclude?
Which is NOT a binary connective?
Evaluate: P ∧ Q where P = T and Q = F.
Wvaluate: (P → Q) ∧ (Q → P) where P = T and Q = F.
In propositional logic, the XOR (exclusive OR) connective yields a...
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