Examples of Converse, Inverse, and Contrapositive Statements

📚 Quick Study Guide

• 📍 Conditional Statement: A statement in the form 'If p, then q,' denoted as $p \rightarrow q$.
• 🔄 Converse: Formed by swapping the hypothesis (p) and conclusion (q) of the conditional statement: $q \rightarrow p$.
• ↩️ Inverse: Formed by negating both the hypothesis (p) and conclusion (q) of the conditional statement: $\neg p \rightarrow \neg q$.
• 💫 Contrapositive: Formed by swapping and negating both the hypothesis (p) and conclusion (q) of the conditional statement: $\neg q \rightarrow \neg p$.
• 💡 Key Point: A conditional statement and its contrapositive are logically equivalent. The converse and inverse are also logically equivalent.

Practice Quiz

1. What is the converse of the statement: 'If it is raining, then the ground is wet'?

   1. If the ground is wet, then it is raining.
   2. If it is not raining, then the ground is not wet.
   3. If the ground is not wet, then it is not raining.
   4. If it is raining, then the ground is not wet.

2. What is the inverse of the statement: 'If I study, then I will pass the exam'?

   1. If I pass the exam, then I studied.
   2. If I do not study, then I will not pass the exam.
   3. If I do not pass the exam, then I did not study.
   4. If I study, then I will not pass the exam.

3. What is the contrapositive of the statement: 'If a shape is a square, then it has four sides'?

   1. If a shape has four sides, then it is a square.
   2. If a shape does not have four sides, then it is not a square.
   3. If a shape is not a square, then it does not have four sides.
   4. If a shape has four sides, then it is not a square.

4. Which of the following is logically equivalent to the statement: 'If I am happy, then I sing'?

   1. If I sing, then I am happy.
   2. If I am not happy, then I do not sing.
   3. If I do not sing, then I am not happy.
   4. If I sing, then I am not happy.

5. What is the inverse of 'If x > 5, then y < 10'?

   1. If y < 10, then x > 5.
   2. If x ≤ 5, then y ≥ 10.
   3. If y ≥ 10, then x ≤ 5.
   4. If x > 5, then y ≥ 10.

6. Identify the contrapositive of the statement: 'If it is a bird, then it can fly.'

   1. If it can fly, then it is a bird.
   2. If it is not a bird, then it cannot fly.
   3. If it cannot fly, then it is not a bird.
   4. If it can fly, then it is not a bird.

7. What is the converse of 'If I eat too much, I feel sick'?

   1. If I feel sick, I eat too much.
   2. If I do not eat too much, I do not feel sick.
   3. If I do not feel sick, I did not eat too much.
   4. If I eat too much, I do not feel sick.