Download indirect and transitive reasoning ()

AP English Language & Composition
Practice with “Indirect Reasoning”
Syllogism
Premise 1: Everyone driving at 80 mph is breaking the law.
Premise 2: But John is not breaking the law.
Conclusion: Therefore, John is not driving at 80 mph.
x - John
driving at
80 mph
Conditional
p → q: If one drives at 80 mph, one is breaking the law.
~q: But John is not breaking the law.
∴ ~p: John is not driving at 80 mph.
breaking the law
1.
Directions: Convert the diagram into two forms of written argument—a conclusion drawn from
premises (syllogism) and a conclusion drawn from a conditional statement. Note that the negation is in
a different spot.
AP Lang
students
students who must
x
take English III
Dayneisha
Syllogism
Premise 1: AP Lang students do not need to take English III
Premise 2: Dayneisha is an AP Lang student.
Conclusion: Therefore, Dayneisha does not need to take
English III.
Conditional
p → ~q: If a student is in AP Lang, then s/he does not take
English III.
p: Dayneisha is in AP Lang.
∴ ~q: Dayneisha does not take English III.
2.
Directions: Draw the proper conclusion and give the corresponding diagram.
If the operation is addition or multiplication, then the associative law holds. For the operation
given, the associative law does not hold. We can thus conclude that . . .
3.
Directions: Explain why the following argument is invalid. Draw the corresponding diagram.
Premise 1: All plastic toys are unbreakable.
Premise 2: This yellow truck is not plastic.
Conclusion: Therefore, this yellow truck is not unbreakable.
AP English Language & Composition
Practice with “Transitive Reasoning”
breaking the law
Syllogism
Premise 1: Everyone driving at 80 mph is speeding.
Premise 2: Everyone speeding is breaking the law.
Conclusion: So everyone driving at 80 mph is breaking the law.
speeding
driving at
80 mph
Conditional
p → q: If one drives at 80 mph, then one is speeding.
q → r: If one is speeding, then one is breaking the law.
(∴ p → r)
p: Bob drives at 80 mph.
∴ r: Bob is breaking the law.
4.
Directions: Convert the diagram into two forms of written argument—a conclusion drawn from
premises (syllogism) and a conclusion drawn from a conditional statement.
real numbers
rational
numbers
even
integers
multiples
of 6
Syllogism
Premise 1: All multiples of 6 are even integers.
Premise 2: All even integers are rational numbers.
Premise 3: All rational numbers are real numbers.
Conclusion: All multiples of 6 are real numbers.
Conditional
p → q: If a number is a multiple of 6, then it is an even integer.
q → r: If a number is an even integer, then it is rational.
r → s: If a number is rational, then it is real.
p: 36 is a multiple of 6.
∴ s: 36 is a real number.
5.
Note: A ∩ B is basic symbolism for saying: some elements of group A are in group B.
Task: If A ∩ B and B ∩ C, can you conclude that A ∩ C ? Draw a diagram to show that this conclusion
could be false.
6.
Explain why the following argument is invalid. Draw the corresponding diagram.
Premise 1: Some plastic toys are yellow.
Premise 2: Some yellow toys are on the floor.
Conclusion: Some plastic toys are on the floor.