Working with Related Conditionals Topic Index | Geometry Index | Regents Exam Prep Center

Answer the following questions dealing with logic and related conditionals.

 1. Which of the following statements is the converse of "If the moon is full, then the vampires are prowling."? Choose one:  If the vampires are prowling, then the moon is full. If the moon is not full, then the vampires are  prowling. If the vampires are not prowling, then the moon is not full. Explanation The converse switches the IF and THEN portions of the sentence.

 2. Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively."? Choose one: If you reason deductively, then you understand geometry. If you understand geometry, then you reason deductively. If the do not reason deductively, then you understand geometry. Explanation Inverse adds NOT to both parts of the original sentence. Remember, two NOTS together cancel each other out.

 3. Which of the following statements is logically equivalent to  "If you live in a mansion, then you have a big heating bill."? Choose one: If you have a big heating bill, then you live in a mansion. If you do not live in a mansion, then you do not have a big heating bill. If you do not have a big heating bill, then you do not live in a mansion. Explanation The original statement is logically equivalent to its contrapositive.

 4. Which of the following statements is the converse of "You cannot skateboard if you do not have a sense of balance."? Choose one: If you cannot skateboard, then you do not have a sense of balance. If you do not have a sense of balance, then you cannot skateboard. If you skateboard, then you have a sense of balance. Explanation Be careful here.  The IF part of the sentence is not at the beginning of the sentence.  Rearrange it first. Converse switches IF and THEN.

 5. Which of the following statements is the contrapositive of  "If you understand logic, you will be a good consumer."? Choose one: If you are a good consumer, then you understand logic. If you are not a good consumer, then you do not understand logic. If you do not understand logic, then you will not be a good consumer. Explanation Contrapositive switches IF and THEN and also adds NOT to both sides.

 6. Which of the following statements is the inverse of  "If it rains, then I do not go fishing."? Choose one: If I go fishing, then it does not rain. If I do not go fishing, then it rains. If it does not rain, then I go fishing. Explanation Inverse adds NOT to both portions of the sentence.

 7. Which of the following statements is the inverse of "Our pond floods whenever there is a thunderstorm."? Choose one: If there is a thunderstorm, then our pond floods. If we do not get a thunderstorm, then our pond does not flood. If our pond does not flood, then we did not get a thunderstorm. Explanation Be careful!  The IF part of this sentence is AFTER the word "whenever". It really reads "If there is a thunderstorm, then our pond floods." Inverse adds NOT to both parts of the sentence.

 8. Which of the following statements is logically equivalent to  "The solution is easy if you read the question carefully."? Choose one: If you do not read the question carefully, the solution is hard. If the solution is easy, then you read the question carefully. If the solution is hard, then you did not read the question carefully. Explanation Be careful!  Notice where the IF is located. The original sentence and the contrapositive are logically equivalent. Contrapositive will switch IF and THEN and also add NOT to both parts.

 9. Which of the following statements is the contrapositive of "If a polygon has four sides, then it is called a quadrilateral."? Choose one: If a polygon is called a quadrilateral, then it has four sides. If a polygon is not called a quadrilateral, then it does not have four sides. If a polygon does not have four sides, then it is not called a quadrilateral. Explanation Contrapositive will switch IF and THEN and also add NOT to both parts.

 10. The inverse of the converse of a conditional statement is the _____. Choose one: converse inverse contrapositive Explanation The converse will switch IF and THEN. The inverse will add NOT to both parts. The contrapositive does BOTH. Combining inverse and converse gives the contrapositive.

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