Use The Law Of Detachment to draw a conclusion:
2. If The football team wins on Friday night, then practice is canceled for monday.
The football team won by 7 points.
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i can't draw it but i can give you some knowledge
Let's look at Law of detachment first.
If p and (p implies q), then we conclude q.
Remember both parts of the hypothesis MUST BE TRUE.
So, let's look at a couple of statements.
p: This toy is a truck.
q: This toy has 4 wheels.
Rememeber p implies q means "If p, then q."
So let's substitute. If this toy is a truck, then it has 4 wheels.
Suppose "The toy is a truck." is true. And suppose "if this toy is a truck, then it has 4 wheels" is also true.
What can you conclude? Well, you can conclude that the toy has 4 wheels. That's the Law of Detachment. It's "sort of like" substitution.
Now, let's look at Law of Syllogism.
Here you have 3 statements: p, q, & r. Notice that in the Law of Detachment you only had 2 statements to work with.
Example: p: Mary is shorter than Debbie.
q: Debbie is shorter than Joan.
r: Joan is shorter than Maria.
If (p implies q) and (q implies r), then we conclude (p implies r).
p implies q: If Mary is shorter than Debbie, then Debbie is shorter than Joan.
q implies r: If Debbie is shorter than Joan, then Joan is shorter than Maria.
We conclude that p implies r. So by Law of Syllogism,
If Mary is shorter than Debbie, then Joan is shorter than Maria.
This is like the Transitive Property.
A key difference to remember is that Detachment works with only 2 statements while Syllogism works with 3 statements.