Law of Syllogism Worksheet
A Grade 11 math worksheet covering the Law of Syllogism with various question types.
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Law of Syllogism Worksheet
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Read each question carefully and answer to the best of your ability. This worksheet assesses your understanding of the Law of Syllogism.
1. Which of the following best describes the Law of Syllogism?
If p → q and q → r are true, then p → r is true.
If p → q is true, then ¬q → ¬p is true.
If p → q is true, and p is true, then q is true.
If p is true, then p is true.
2. Given the statements: If it rains, the ground gets wet. If the ground gets wet, the plants grow. What valid conclusion can be drawn?
If it rains, the plants grow.
If the plants grow, it rained.
The ground is wet.
It does not rain.
3. The Law of Syllogism states that if two conditional statements are true, and the conclusion of the first statement is the hypothesis of the second statement, then a new conditional statement can be formed by combining the of the first statement and the conclusion of the statement.
4. Given: If a shape is a square (p), then it is a rectangle (q). If a shape is a rectangle (q), then it is a quadrilateral (r). By the Law of Syllogism, the conclusion is: If a shape is a square (p), then it is a (r).
5. Explain in your own words how the Law of Syllogism is used in logical reasoning.
6. The Law of Syllogism can be applied to any two conditional statements, regardless of whether their parts overlap.
True
False
7. If p → q is true and r → p is true, then by the Law of Syllogism, r → q is a valid conclusion.
True
False
Match the logical statement on the left with its equivalent on the right, assuming the Law of Syllogism applies.
8. If A → B and B → C
a. If it's a dog, it's an animal
9. If it's a mammal, it's an animal; if it's a dog, it's a mammal
b. A → C
10. Construct a valid argument using the Law of Syllogism with three different conditional statements.