Take Note Property: Law of Syllogism

Symbols

Example

If it is July, then you are on summer vacation.

If you are on summer vacation, then you work at a smoothie shop.

You conclude: If it is July, then you work at a smoothie shop.

Problem 2 Using the Law of Syllogism

What can you conclude from the given information?

1. Given: If a figure is a square, then the figure is a rectangle.

   If a figure is a rectangle, then the figure has four sides.

   If a figure is a square, then the figure is a rectangle.

   If a figure is a rectangle, then the figure has four sides.

   The conclusion of the first statement is the hypothesis of the second statement, so you can use the Law of Syllogism to make a conclusion.

   You conclude: If a figure is a square, then the figure has four sides.

2. Given: If you do gymnastics, then you are flexible.

   If you do ballet, then you are flexible.

   If you do gymnastics, then you are flexible.

   If you do ballet, then you are flexible.

   The statements have the same conclusion. Neither conclusion is the hypothesis of the other statement, so you cannot use the Law of Syllogism. You cannot make a conclusion.

✓ Got It?

2. What can you conclude from the given information? What is your reasoning?

   1. If a whole number ends in 0, then it is divisible by 10.

      If a whole number is divisible by 10, then it is divisible by 5.

   2. If A B → eh b vector  and A D → eh d vector  are opposite rays, then the two rays form a straight angle. If two rays are opposite rays, then the two rays form a straight angle.