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Quizzes > High School Quizzes > Technology

Practice Quiz: Converse, Inverse & Contrapositive

Practice problems with guided explanations and answers

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art illustrating the engaging Logic Flip Challenge trivia for high school students.

What is the contrapositive of 'If p, then q'?
If not p, then not q
If p, then q
If not q, then not p
If q, then p
The contrapositive is formed by negating both the hypothesis and the conclusion and then reversing their order. This transformation always yields a statement that is logically equivalent to the original implication.
What is the converse of 'If p, then q'?
If p, then q
If q, then p
If not q, then not p
If not p, then not q
The converse of a conditional statement is created by simply swapping the hypothesis and the conclusion. While it mirrors the structure of the original, it is not necessarily equivalent in truth value.
What is the inverse of 'If p, then q'?
If p, then q
If q, then p
If not q, then not p
If not p, then not q
The inverse is obtained by negating both components (p and q) of the original statement. Although it looks similar to the contrapositive, it does not guarantee logical equivalence with the original implication.
Which transformed statement is logically equivalent to the implication 'If p, then q'?
If not q, then not p
If not p, then not q
If p, then q
If q, then p
The contrapositive, which is 'If not q, then not p', is always logically equivalent to the original conditional statement. This property distinguishes it from the converse and inverse transformations.
If the statement 'If it is sunny, then we go to the park' is true, which of the following must also be true?
If we do not go to the park, then it is not sunny
None of the above
If it is not sunny, then we do not go to the park
If we go to the park, then it is sunny
The contrapositive of the given statement is logically equivalent to it. Therefore, if 'If it is sunny, then we go to the park' is true, its contrapositive 'If we do not go to the park, then it is not sunny' must also be true.
Consider the statement 'If it rains, then the ground gets wet.' What is the inverse of this statement?
If the ground gets wet, then it rains
If the ground does not get wet, then it does not rain
If it does not rain, then the ground does not get wet
If it rains, then the ground does not get wet
The inverse of a conditional statement is derived by negating both the hypothesis and the conclusion. While this transformation alters the statement, it is not generally equivalent to the original implication.
Given the statement 'If a student studies, then they pass the exam,' what is the contrapositive?
If a student passes the exam, then they studied
If a student does not pass the exam, then they did not study
If a student studies, then they do not pass the exam
If a student does not study, then they do not pass the exam
The contrapositive is formed by negating and reversing the parts of the original statement. Because it preserves the truth value, option A is the correct contrapositive.
Which of the following is the correct converse of 'If a number is even, then it is divisible by 2'?
If a number is not divisible by 2, then it is not even
If a number is divisible by 2, then it is even
If a number is odd, then it is not divisible by 2
If a number is even, then it is not divisible by 2
The converse is obtained by swapping the hypothesis and conclusion of the original statement. Option A directly reflects this reversal.
If 'If a person is a teacher, then they have a degree' is true, which is its contrapositive?
If a person has a degree, then they are a teacher
If a person is a teacher, then they do not have a degree
If a person does not have a degree, then they are not a teacher
If a person is not a teacher, then they do not have a degree
The contrapositive is formed by negating and reversing the original components. This means that if the original statement is true, its contrapositive 'If a person does not have a degree, then they are not a teacher' must also be true.
Which of the following, when applied to 'If it is snowing, then school is canceled,' might result in a statement that is not necessarily true?
None of the above
Contrapositive: If school is not canceled, then it is not snowing
Original statement: If it is snowing, then school is canceled
Converse: If school is canceled, then it is snowing
The contrapositive of a true implication is always true, whereas the converse is not guaranteed to share the same truth value as the original statement. Therefore, the converse in option B might not be true even if the original statement holds.
What is the correct converse of 'If a figure is a triangle, then it has three sides'?
If a figure is not a triangle, then it does not have three sides
If a figure has more than three sides, then it is not a triangle
If a figure has three sides, then it is a triangle
If a figure does not have three sides, then it is a triangle
The converse reverses the hypothesis and the conclusion of the original statement. In this case, the correct reversal is provided by option A.
What is the inverse of 'If a machine is well-maintained, then it operates efficiently'?
If a machine is not well-maintained, then it does not operate efficiently
If a machine operates efficiently, then it is well-maintained
If a machine is not maintained, then it operates efficiently
If a machine operates inefficiently, then it is not well-maintained
The inverse is created by negating both the hypothesis and the conclusion of the original statement. Option A correctly demonstrates this transformation.
Which of the following statements is logically equivalent to 'If a substance is acidic, then it turns litmus paper red'?
If a substance is not acidic, then it turns litmus paper red
If a substance turns litmus paper red, then it is acidic
If a substance does not turn litmus paper red, then it is not acidic
If a substance is acidic, then it does not turn litmus paper red
The contrapositive of any implication is logically equivalent to the original statement. Option A is the contrapositive of the given statement, making it the correct answer.
Determine the converse of 'If someone is a bachelor, then they are unmarried.'
If someone is unmarried, then they are married
If someone is married, then they are not a bachelor
If someone is a bachelor, then they are married
If someone is unmarried, then they are a bachelor
The converse is obtained by switching the original hypothesis and conclusion. Therefore, option A accurately represents the converse of the provided statement.
What is the correct contrapositive of 'If an animal is a bird, then it can fly'?
If an animal is not a bird, then it cannot fly
If an animal cannot fly, then it is a bird
If an animal cannot fly, then it is not a bird
If an animal can fly, then it is a bird
The contrapositive requires negating both parts of the statement and then switching them. Option A correctly applies this rule, resulting in a statement that is logically equivalent to the original.
Consider the statement 'If a car is well-maintained, then it runs smoothly.' Which of the following is the correct contrapositive?
If a car is well-maintained, then it does not run smoothly
If a car is not well-maintained, then it does not run smoothly
If a car runs smoothly, then it is well-maintained
If a car does not run smoothly, then it is not well-maintained
To form the contrapositive, one must negate both the hypothesis and the conclusion and then swap their positions. This process results in option A, which is logically equivalent to the original statement.
Which of the following pairs of statements are logically equivalent?
'If p then q' and 'If not q then not p'
'If p then q' and 'If q then p'
'If p then q' and 'If q then not p'
'If p then q' and 'If not p then not q'
An implication is always logically equivalent to its contrapositive. Option A shows this exact pair, making them the only equivalent pair among the choices.
Consider the conditional statement 'If a software program is bug-free, then it runs efficiently.' Which of the following represents its inverse?
If a software program runs efficiently, then it is bug-free
If a software program does not run efficiently, then it is not bug-free
If a software program is not bug-free, then it does not run efficiently
If a software program is bug-free, then it does not run efficiently
The inverse is derived by negating both the hypothesis and the conclusion of the statement. Option A accurately reflects this transformation.
A statement and its contrapositive share the same truth value. Which of the following implications exemplifies this principle?
If a bicycle has gears, then it cannot shift speeds and If a bicycle cannot shift speeds, then it has gears
If a bicycle can shift speeds, then it has gears and If a bicycle has gears, then it can shift speeds
If a bicycle has gears, then it can shift speeds and If a bicycle cannot shift speeds, then it does not have gears
If a bicycle does not have gears, then it cannot shift speeds and If a bicycle can shift speeds, then it has gears
A statement and its contrapositive always share the same truth value. Option A correctly demonstrates this by pairing the original implication with its proper contrapositive.
Which of the following represents a common misunderstanding when transforming implications into their inverses or converses?
Understanding that the converse 'If q then p' may not be equivalent to the original
Assuming that the inverse 'If not p then not q' always holds the same truth value as the original 'If p then q'
Using logical transformations to analyze conditional statements
Recognizing that the contrapositive is always logically equivalent to the original statement
A common error in reasoning is to assume that the inverse of an implication has the same truth value as the original statement. Option A highlights this misconception, as only the contrapositive is guaranteed to be logically equivalent.
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Study Outcomes

  1. Analyze the differences between converse, inverse, and contrapositive statements.
  2. Apply logical reasoning to solve dynamic logic puzzles.
  3. Evaluate complex statements to identify key logical relationships.
  4. Develop strategies to recognize and correct reasoning errors.
  5. Assess logic problems to enhance critical thinking skills.

Converse, Inverse & Contrapositive Cheat Sheet

  1. Understand the Converse Statement - Swap the hypothesis and conclusion to see if the logic still holds up. For example, turning "If it rains, then the ground is wet" into "If the ground is wet, then it rains" can reveal hidden assumptions. This twist trains you to catch sneaky logical switches quickly! What is Converse Statement | Examples, Inverse and Contrapositive - GeeksforGeeks
  2. Learn the Inverse Statement - Negate both parts of the original statement and test its truth. So "If it does not rain, then the ground is not wet" might fail when sprinklers are involved! Playing with negations makes your logic skills nearly unstoppable. What is Converse Statement | Examples, Inverse and Contrapositive - GeeksforGeeks
  3. Master the Contrapositive Statement - Flip and negate to form the contrapositive: "If the ground is not wet, then it does not rain." This version is always logically equivalent to the original, making it a proof-writer's best friend. Spotting contrapositives is like having a secret weapon in math battles! What is Converse Statement | Examples, Inverse and Contrapositive - GeeksforGeeks
  4. Recognize Logical Equivalence - Remember that a conditional statement and its contrapositive share the same truth value. If one is true, the other is too; if one is false, the other follows suit. This powerful fact lets you swap statements without breaking a sweat. What Are the Converse, Contrapositive, and Inverse? - ThoughtCo
  5. Differentiate Truth Values - Just because the original statement is true doesn't mean its converse or inverse will be. Each variant needs its own independent check. Learning to test them separately will make you a logic detective! What is Converse Statement | Examples, Inverse and Contrapositive - GeeksforGeeks
  6. Practice with Examples - Dive into varied scenarios like "If a shape is a square, then it has four equal sides" and tweak them. The more you play, the more patterns you'll spot. Real practice turns theory into automatic brain reflexes! Converse, Inverse, and Contrapositive Examples (Video) - Mometrix
  7. Use Mnemonic Devices - Keep "Converse swaps, Inverse negates, Contrapositive swaps and negates" ringing in your head. A catchy phrase sticks better than dry definitions. Turn it into a chant for instant recall during exams! Converse, Inverse, and Contrapositive Examples (Video) - Mometrix
  8. Understand Contraposition - This principle states a conditional statement is true if and only if its contrapositive is true. It's the cornerstone of many mathematical proofs and logical arguments. Embracing contraposition gives you VIP access to advanced reasoning! Contraposition - Wikipedia
  9. Explore Real-World Applications - From proving theorems to optimizing algorithms, these logical forms are everywhere. Recognizing them in code and proofs makes complex ideas click. You'll start spotting logic patterns in daily life like a super sleuth! Converse, Inverse, and Contrapositive Examples (Video) - Mometrix
  10. Test Your Knowledge - Challenge yourself with flashcards and quizzes to pinpoint weak spots and celebrate strengths. Regular self-testing cements concepts far better than passive reading. Ready, set, quiz! Converse, Inverse, Contrapositive Flashcards - Quizlet
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