What is the difference between Law of Detachment and The Law of Syllogism ? pLEASE provide an example of both thx.
The law of detachment is the first form of deductive reasoning. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. The most basic form is listed below:
1.P�¨Q (conditional statement)
2.P (hypothesis stated)
3.Q (conclusion deduced)
In deductive reasoning, we can conclude Q from P by using the law of detachment.[2] However, if the conclusion (Q) is given instead of the hypothesis (P) then there is no valid conclusion.
The following is an example of an argument using the law of detachment in the form of an if-then statement:
1.If an angle A>90�‹, then A is an obtuse angle.
2.A=120�‹
3.A is an obtuse angle.
Since the measurement of angle A is greater than 90�‹, we can deduce that A is an obtuse angle.
If jay doesnt work hard, then he won 't start the game. If he doesnt start the game, then he will quit the team.
if jay doesnt work hard then he will quit the team
The Law of Detachment and the Law of Syllogism are two important principles in deductive reasoning, which is a fundamental aspect of logic. These principles help determine the validity of logical arguments and draw conclusions based on given premises.
1. Law of Detachment:
The Law of Detachment states that if a conditional statement ("if-then") is true, and the hypothesis (the "if" part) is true, then the conclusion (the "then" part) can be inferred as true.
In simpler terms, if we have the statement "If A, then B," and we know that A is true, then we can conclude that B is also true.
Example:
If it is raining, then the ground is wet.
Given that it is raining (A is true), we can use the Law of Detachment to conclude that the ground is wet (B is true).
2. Law of Syllogism:
The Law of Syllogism states that if two conditional statements are given, where the conclusion of the first statement matches the hypothesis of the second statement, then we can combine these two statements to form a new valid conclusion.
In simpler terms, if we have the statements "If A, then B" and "If B, then C," then we can logically deduce the conclusion "If A, then C."
Example:
If it is sunny, then Sarah goes to the park. (If A, then B)
If Sarah goes to the park, then she plays on the swings. (If B, then C)
Using the Law of Syllogism, we can combine these two statements to form a new conclusion:
If it is sunny, then Sarah plays on the swings. (If A, then C)
To summarize:
The Law of Detachment deals with a single conditional statement, where the truth of the hypothesis leads to the truth of the conclusion.
The Law of Syllogism combines two conditional statements to form a new logical conclusion.
Both laws provide methods for drawing logical conclusions based on given premises and are vital in formal logic and deductive reasoning.