Page 184 - Math Course 2 (Book 2)

Deductive Reasoning
Mo. 12

Lesson 4 Key Concept

KEY CONCEPTS: Law of Detachment

1. Use the Law of Detachment. Word If p → q is true and p is true, then q is
2. Use the Law of Syllogism also true.

Symbols [( p → q ) ⋀ p ] → q

MO. 12 - L4a

Laws of Detachment and Law of Syllogism
Syllogism Word If p → q and q → r are true, then p → r
is also true.

Vocabulary A-Z Symbols [( p → q ) ⋀ ( p → r ) ] → ( p → r )

Let us learn some vocabulary Example If 2x = 14, then x = 7 and if x = 7, then
1
1
= . Therefore, if 2x = 14 then
x
7
deductive reasoning 1 1
7
Unlike inductive reasoning, which uses examples = .
x
to make a conjecture, deductive reasoning uses
facts, rules, definitions, or properties to reach
logical conclusions.
Since you have dog house, I deduce that you Let’s Begin
have a dog.

Since you have a family, I deduce that you
have a wife. Determine Valid Conclusions

law of detachment Examples
Used to draw conclusions from true conditional
statements, it states that if p → q is true and p is
true, then q must be true. The following is a true conditional. Determine
whether the conclusion is valid based on the given
If an angle is obtuse, then it cannot be acute. information. Explain your reasoning. If two seg-
Angle A is obtuse. ments are congruent and the second segment is
congruent to a third segment, then the first seg-
Therefore Angle A cannot be acute. ment is also congruent to the third segment.
Given: WX ≅ UV; UV ≅ RT
law of syllogism Conclusion: WX ≅ RT
Used to draw conclusions from true conditional
statements, it states that if p → q and q → r are The hypothesis states that WX = UV and UV ≅ RT
both true, then p → r is true.
If the electric power is cut, then the refrigerator does Since the conditional is true and
not work. Answer the hypothesis is true, the
If the refrigerator does not work, then the food is conclusion is valid.
spoiled.
So if the electric power is cut, then the food is spoiled

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