Question

the law of detachment
this law of logic states that if you start with a hypothesis of a true conditional, then the conclusion is also true.
sample conditional statement:
hypothesis → conclusion
if a figure is a square, then it is a rectangle.
this figure is a square. the hypothesis is true.
conclusion: the figure is a rectangle.
use the law of detachment to write a conclusion.

1. if a dog goes out to play in the woods, then the dog will get dirty.

kari’s dog spot goes out to play in the woods.
conclusion:

1. if an animal is an ant, then the animal is an insect.

a carpenter ant is a type of ant.
conclusion:
the law of syllogism
this law of logic allows you to put a series of conditional statements together.
sample if it is 5:00 p.m., then it is almost time for dinner.
if it is almost time for dinner, then i should stop watching tv.
if the conditionals are true, then you can conclude the following:
if it is 5:00 p.m., then i should stop watching tv.
use the law of syllogism to complete the conclusion.

1. if it is raining, then the sidewalk will be wet.

if the sidewalk is wet, then the sidewalk will be slippery.
if it is raining,

1. if the temperature is below 58°f, then the heater will come on.

if the heater comes on, then the air inside will be dry.
if the temperature is below 58°f, then

Explanation:

Step1: Identify hypothesis and conclusion for Law of Detachment in problem 1

The conditional is "If a dog goes out to play in the woods, then the dog will get dirty." The hypothesis "Kari’s dog Spot goes out to play in the woods" is true.

Step2: Apply Law of Detachment

Since the hypothesis is true, the conclusion of the conditional is true.

Step3: Identify hypothesis and conclusion for Law of Detachment in problem 2

The conditional is "If an animal is an ant, then the animal is an insect." The hypothesis "A carpenter ant is a type of ant" is true.

Step4: Apply Law of Detachment

Since the hypothesis is true, the conclusion of the conditional is true.

Step5: Apply Law of Syllogism in problem 3

The first conditional is "If it is raining, then the sidewalk will be wet." The second is "If the sidewalk is wet, then the sidewalk will be slippery." By the Law of Syllogism, if the first - two are true, then "If it is raining, then the sidewalk will be slippery".

Step6: Apply Law of Syllogism in problem 4

The first conditional is "If the temperature is below 58°F, then the heater will come on." The second is "If the heater comes on, then the air inside will be dry." By the Law of Syllogism, if the first - two are true, then "If the temperature is below 58°F, then the air inside will be dry".

Answer:

1. Kari’s dog Spot will get dirty.
2. A carpenter ant is an insect.
3. the sidewalk will be slippery.
4. the air inside will be dry.