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Multiple Choice
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Using the truth table method, indicate whether the following arguments are valid or invalid.



1

p v q
~p
∴q
A)Valid
B)Invalid
2

p → q
q → r
∴p & r
A)Valid
B)Invalid
3

~(a → ~b)
∴b
A)Valid
B)Invalid
4

p v q
p → r
q → r
∴r
A)Valid
B)Invalid
5

(p & q) → ~r
q → r
q
∴~(p & q)
A)Valid
B)Invalid
6

p v (~q → r)
r & q
p → ~r
~q → r
A)Valid
B)Invalid
7

If Bill is President then Al is Vice President. Bill is not President. So, Al is not Vice President.
A)Valid
B)Invalid
8

If I have a clean driving record, I'll receive a discount on my auto insurance. I do have a clean driving record. So, I get the discount.
A)Valid
B)Invalid
9

It's not true that pigeons are reptiles or that pigeons are fish. If pigeons aren't reptiles, then pigeons aren't lizards. So, pigeons must not be lizards.
A)Valid
B)Invalid
10

If Pinkerton does not show then Quail will play third base. Either Wallace will not play catcher or Pinkerton does not show. Hence, if Wallace will play catcher then Quail will play third base.
A)Valid
B)Invalid
11

It's not the case that both Alex and Sally are invited. If Alex is invited, then Harold is invited. But it is not the case that Harold is invited. Thus, Sally must be invited.
A)Valid
B)Invalid
12

Either it's true that if Jim is late then Nancy is late, or they're driving in separate cars. Its not the case that either Nancy is late or they're driving in separate cars. Thus, if Nancy is not late then Jim is not late.
A)Valid
B)Invalid
13

It's not the case that if Sam makes the team then Frank will make the team. It's not the case that either Sam or Bill will make the team. Thus, Bill won't make the team and Frank will make the team.
A)Valid
B)Invalid
14

If Charles gets the account he'll get that promotion. If he gets the promotion, he's moving to Colorado. If he moves to Colorado, he won't sell his truck. If he won't sell his truck, he won't have enough money to buy a new suit. If he doesn't have the cash to buy a new suit, he'll look awful. If he looks awful, he won't impress the client. If he doesn't impress the client he won't get the account, so if he gets the account, then he won't get the account.
A)Valid
B)Invalid







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