Logic: Converse, Inverse, Contrapositive

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the converse of the statement 'If two integers are equal, then their squares are equal'?

  • If the squares of two integers are not equal, then the two integers are not equal.
  • If two integers are equal, then their squares are not equal.
  • If two integers are not equal, then their squares are equal.
  • If the squares of two integers are equal, then the two integers are equal. (correct)

Which statement represents the inverse of the original statement?

  • If two integers are equal, then their squares are equal.
  • If two integers are not equal, then their squares are not equal. (correct)
  • If two integers are not equal, then their squares are equal.
  • If two integers are equal, then their squares are not equal.

What is the contrapositive of the statement 'If two integers are equal, then their squares are equal'?

  • If the squares of two integers are equal, then the two integers are equal.
  • If the squares of two integers are not equal, then the two integers are not equal. (correct)
  • If two integers are equal, then their squares are not equal.
  • If the squares of two integers are not equal, then the two integers are equal.

Which of the following is NOT true about the relationship between a statement and its contrapositive?

<p>A statement and its contrapositive can have different meanings. (B)</p> Signup and view all the answers

What is false about the inverse of the statement 'If two integers are equal, then their squares are equal'?

<p>It states that unequal integers have equal squares. (C)</p> Signup and view all the answers

Flashcards

Converse statement

If q is true, then p is true.

Inverse statement

If not p, then not q.

Contrapositive statement

If not q, then not p.

Original statement

If p, then q.

Signup and view all the flashcards

Integer squares

If two integers are equal, then their squares will also be equal.

Signup and view all the flashcards

Study Notes

Converse, Inverse, and Contrapositive

  • Converse: If the squares of two integers are equal, then the two integers are equal.
  • Inverse: If two integers are not equal, then their squares are not equal.
  • Contrapositive: If the squares of two integers are not equal, then the two integers are not equal.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser