math Law of Syllogism and Law of Detachment

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What is the difference between Law of Detachment and The Law of Syllogism ? pLEASE provide an example of both thx.

• math Law of Syllogism and Law of Detachment -

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.

• math Law of Syllogism and Law of Detachment -

If jay doesnt work hard, then he won 't start the game. If he doesnt start the game, then he will quit the team.

• math Law of Syllogism and Law of Detachment -

if jay doesnt work hard then he will quit the team

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