Deductive Args

Here are the answers to the handout on deductive arguments that we went over in class.

1) All bats are mammals.
All mammals live on earth.
All bats live on earth.

Valid, Sound

2) All students in here are mammals.
All humans are mammals.
All students in here are humans.

Invalid, Unsound (because it's invalid)

3) (from Stephen Colbert)
Bush is either a great prez or the greatest prez.
Bush isn’t a great prez.
Bush is the greatest prez.

Valid, Unsound (questionable premises)

4) Sean either went to school or something kept him from going to school.
Nothing kept Sean from going to school.
Sean went to school.

Valid, Sound

5) Some people are funny.
Sean is a person.
Sean is funny.

Invalid, Unsound (because it's invalid)

6) If Sean sings, then students cringe.
Sean is singing right now.
Students are cringing right now.

Valid, Unsound (false second premise: I'm not singing right now)

7) It either rains or Sean swims.
If it rains, then Sean gets wet.
If Sean swims, then he gets wet.
I get wet.

Valid, Unsound (false first premise: sometimes it isn't raining and I'm not swimming)

8) If Sean sings, then students cringe.
Students are cringing right now.
Sean is singing right now.

Invalid, Unsound (it's invalid, and false second premise)

9) All email forwards are annoying.
Some email forwards are false.
Some annoying things are false.

Valid, Unsound (questionable first premise)

10) If Sean sings, then students cringe.
Sean isn't singing right now.
Students aren't cringing right now.

Invalid, Unsound (it's invalid)

11) All bats are mammals.
All bats have wings.
All mammals have wings.

Invalid, Unsound (because it's invalid)

12) If Sean sings, then students cringe.
Students aren't cringing right now.
Sean isn't singing right now.

Valid, Sound

13) All dads have beards.
All bearded people are mean.
All dads are mean.

Valid, Unsound (false premises)

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