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Notes
Practice Problems
Are the following valid using the Law of Syllogism?
\(\textbf{1)}\) If Johnny runs, he will lose weight. If he loses weight, he will be healthier.
Therefore If Johnny runs, he will be healthier.
\(\textbf{2)}\) If you study, you will pass the test. You don’t study.
Therefore you won’t pass the test.
\(\textbf{3)}\) If a student practices, they will improve their skills. If a student practices, they will succeed in the recital.
Therefore If a student improves their skills, they will succeed in the recital.
\(\textbf{4)}\) If it rains, the ground will get wet. If the ground gets wet, flowers will bloom.
Therefore, if it rains, flowers will bloom.
\(\textbf{5)}\) If you save money, you will have more for retirement. If you have more for retirement, you will be financially secure.
Therefore, if you save money, you will be financially secure.
\(\textbf{6)}\) If a bird can fly, it has feathers. If a can migrate, it has feathers.
Therefore, if a bird can fly, it can migrate.
\(\textbf{7)}\) If you exercise regularly, you will be healthy. If you are healthy, you will live longer.
Therefore, if you exercise regularly, you will live longer.
\(\textbf{8)}\) If you don’t water the plant, it will wither. If it withers, it will die.
Therefore, if you don’t water the plant, it will die.
\(\textbf{9)}\) If you don’t study for the exam, you won’t pass. If you don’t pass, you won’t graduate.
Therefore, if you don’t study for the exam, you won’t graduate.
\(\textbf{10)}\) If you eat junk food, you will gain weight. If you gain weight, you will be less healthy.
Therefore, if you eat junk food, you will be less healthy.
Therefore If Johnny runs, he will be healthier.
Therefore you won’t pass the test.
Therefore If a student improves their skills, they will succeed in the recital.
Therefore, if it rains, flowers will bloom.
Therefore, if you save money, you will be financially secure.
Therefore, if a bird can fly, it can migrate.
Therefore, if you exercise regularly, you will live longer.
Therefore, if you don’t water the plant, it will die.
Therefore, if you don’t study for the exam, you won’t graduate.
Therefore, if you eat junk food, you will be less healthy.
See Related Pages\(\)
\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Conditional Statements}\)
\(\,\,\,\,\,\,\,\,\text{Conditional, Converse, Inverse, Contrapositive, Biconditional…}\)
\(\bullet\text{ Law of Detachment}\)
\(\,\,\,\,\,\,\,\,\text{If p then q,}\)
\(\,\,\,\,\,\,\,\,\text{p is true,}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{q is true…}\)
In Summary
We learn about the Law of Syllogism in order to understand how to reason logically and make valid deductions from given information. This law is a crucial tool for critical thinking and problem-solving, and it is often studied in logic and philosophy classes. It also shows up early on in many high school geometry courses to set up the logic behind proofs, specifically the transitive property.
A fun fact about the Law of Syllogism is that it has been studied and used for centuries. It was first formally described by the Greek philosopher Aristotle in his work “Prior Analytics,” which was written in the 4th century BC.
Some related topics to the Law of Syllogism include deductive reasoning, logical fallacies, and propositional logic. Understanding these concepts can help you better understand and apply the Law of Syllogism in your own reasoning and problem-solving.
Topics that use Law of Syllogism
Propositional logic is a branch of mathematical logic that deals with logical statements and the relationships between them. The Law of Syllogism is a key concept in propositional logic, as it allows us to deduce new statements from given statements.
Set theory is a branch of mathematics that deals with sets, which are collections of objects or elements. The Law of Syllogism can be used to deduce new sets from given sets, based on the logical relationships between the elements.
Boolean algebra is a branch of mathematics that deals with logical operations and the manipulation of binary values (0s and 1s). The Law of Syllogism is used in Boolean algebra to deduce new logical statements from given statements.
Graph theory is a branch of mathematics that deals with graphs, which are used to represent relationships between objects or data. The Law of Syllogism can be used to deduce new relationships between objects based on given relationships.
Discrete math is a branch of mathematics that deals with discrete (separated) objects or data, rather than continuous data. The Law of Syllogism is used in discrete math to deduce new statements or relationships from given statements or relationships.
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