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Question 3(Multiple Choice Worth 1 points)

(01.05 MC)

Which statement is logically equivalent to the following conditional statement?

"If it is a rectangle, then it does not have exactly three sides."

If it has exactly three sides, then it is not a rectangle.
If it is not a rectangle, then it has exactly three sides.
If it does not have exactly three sides, then it is a rectangle.
If it is not a rectangle, then it does not have exactly three sides.

1 answer

To find a logically equivalent statement to the conditional "If it is a rectangle, then it does not have exactly three sides," we can apply the concept of contraposition, which states that a conditional statement "If P, then Q" is logically equivalent to "If not Q, then not P."

In this case:

  • Let P be "it is a rectangle."
  • Let Q be "it does not have exactly three sides."

The contrapositive would be: "If it has exactly three sides, then it is not a rectangle."

Now, let's analyze the options:

  1. If it has exactly three sides, then it is not a rectangle. (This is the contrapositive, so it is logically equivalent.)
  2. If it is not a rectangle, then it has exactly three sides. (This is not equivalent.)
  3. If it does not have exactly three sides, then it is a rectangle. (This is not equivalent.)
  4. If it is not a rectangle, then it does not have exactly three sides. (This is not equivalent.)

The correct choice is: If it has exactly three sides, then it is not a rectangle.