Law of Syllogism Worksheet
Explore the Law of Syllogism with this worksheet focusing on logical reasoning and drawing conclusions from conditional statements.
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Law of Syllogism Worksheet
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Read each problem carefully and apply the Law of Syllogism to determine the valid conclusion. If no valid conclusion can be drawn, write 'No valid conclusion'.
1. The Law of Syllogism states that if p → q and q → r are true statements, then is a true statement.
2. The Law of Syllogism is also known as the law of reasoning.
3. For the Law of Syllogism to apply, the of the first conditional statement must be the same as the of the second conditional statement.
For each set of statements, write a valid conclusion using the Law of Syllogism. If no valid conclusion can be drawn, write 'No valid conclusion'.
4. If a polygon is a square, then it is a rectangle. If a polygon is a rectangle, then it has four right angles.
5. If it is raining, then the ground is wet. If the ground is wet, then the plants are happy.
6. If a student studies, then they will pass the test. If a student passes the test, then they will get a good grade.
7. Which of the following correctly applies the Law of Syllogism?
If A then B. If C then B. Conclusion: If A then C.
If A then B. If B then C. Conclusion: If A then C.
If A then B. If A then C. Conclusion: If B then C.
If A then B. If C then D. Conclusion: If A then D.
8. The Law of Syllogism requires that the conclusion of the first statement matches the hypothesis of the second statement.
True
False
9. Consider the following statements: P1: If a number is even, then it is divisible by 2. P2: If a number is divisible by 2, then it ends in 0, 2, 4, 6, or 8. P3: If a number ends in 0, 2, 4, 6, or 8, then it is not odd. Use the Law of Syllogism to draw a conclusion from P1 and P2. Then, use that conclusion and P3 to draw a final conclusion.