Understanding and Evaluating Logical Statements

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 13 | Questions: 20 | Updated: Jan 21, 2026
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Question 1 / 21
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1) Which of the following is a proposition?

Explanation

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

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About This Quiz
Understanding and Evaluating Logical Statements - Quiz

Take simplification to the next level! This quiz challenges you with advanced Karnaugh map problems requiring careful grouping and insight. Try this quiz to push your Boolean algebra skills.

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

Explanation

This is an implication (P → Q).

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3) Which statement matches P ∧ Q?

Explanation

Conjunction requires both parts to be true.

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

Explanation

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

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

Explanation

Biconditional means equivalence of truth values.

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6) Which of these is a tautology?

Explanation

‘P or not P’ is always true.

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7) Which is a contradiction?

Explanation

‘P and not P’ is always false.

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

Explanation

This is a biconditional: outcome tied to studying.

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

Explanation

OR is true if at least one part is true.

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

Explanation

This is the law of the excluded middle.

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

Explanation

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

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

Explanation

The negation of 'All' is 'Some…not'.

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

Explanation

This is a valid syllogism.

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

Explanation

A false premise makes the implication true regardless of conclusion.

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

Explanation

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

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

Explanation

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

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

Explanation

By De Morgan’s Law, NOT(OR) = AND of negations.
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18) Which pair is logically equivalent?

Explanation

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

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

Explanation

This is the fallacy of affirming the consequent.

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

Explanation

Conjunction allows us to infer both P and Q separately.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Which of the following is a proposition?
The statement 'If it rains, then I will take an umbrella' is:
Which statement matches P ∧ Q?
An implication 'If P then Q' is false only when:
The biconditional 'P ↔ Q' is true when:
Which of these is a tautology?
Which is a contradiction?
‘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 true.
The negation of 'All birds can fly' is:
‘All humans are mortal. Socrates is a human. Therefore Socrates is...
The implication 'If the sky is green, then 2+2=5' is true.
The contrapositive of 'If P then Q' is:
‘If it rains, the street is wet. The street is wet, so it rained.’...
Simplify ¬(P∨Q)\neg(P \lor Q)¬(P∨Q).
Which pair is logically equivalent?
‘If P then Q. Q. Therefore P.’ is:
From (P∧Q)(P \land Q)(P∧Q), what can we validly conclude?
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