Logic Homework #1

[Jess]

If anyone is good at logic, I need some help with the homework.

a. Provide a set of sentences that is logically inconsistent.
This is what I had: {All dogs are mortal, Spot is a dog, Spot is not mortal}

b. Provide a set of sentences containing one sentence that is false such that the entire set is logically consistent.
I'm stumped on this one. A set of sentences is logically consistent IF AND ONLY IF every member of the set is true. So if one sentence is false, the entire sentence can't be consistent. I'm sure I should put down "not possible" but I don't know if I can do that...doesn't ask if it's possible or not...and I may be wrong and it is possible.

There are more, which I will post later when I get to them.

[RumblingLambchop]

I think it means something like this: Spot is a dog; Dogs are mortal; Spot is mortal. It isn't logically incorrect, but the second sentence is obviously not true.

[Jess]

Wait, why is the second not true? I'm confused.

[RumblingLambchop]

Oh, I meant to say: Spot is a dog; Dogs are human; Spot is a human.

[Gigablue]

A set of sentences is logically consistent IF AND ONLY IF every member of the set is true.

Actually, a set of sentences is logically consistent if it doesn't contain a contradiction.

I think that you could have this set as an example. I'm not sure though.

{Spot is a dog, All dogs are mortal, All humans are immortal, Spot is mortal}

The third sentence is obviously wrong, but the set doesn't contain a contradiction, therefore it is logically consistent.

[Jess]

If yes, provide an example; if no, explain why

c. Can a deductively valid argument have all false premises and a true conclusion?
Yes:
Birds are mammals.
Dogs can fly
__________________
Dolphins are mammals.

Is that right?

d. Can a deductively valid argument have a conclusion that is logically false?
If a conclusion is logically false, it can't be true. For the argument to be valid, the premises can't be true and the conclusion false. So...I can't really think of whether or not this is possible. This one stumps me :/

[RumblingLambchop]

For the first one, you're right, but do the premises have to relate to the conclusion, like this?:

Tigers have spots
Leopards have stripes
----------------------------
It is possible for animals to have spots or stripes

I was just wondering, because it said "deductively valid", meaning the premises would have to logically lead to the conclusion. Either way, you're right on that one.
For the second one, I'm having a hard time thinking of an example that would work for the second, so I'm leaning towards what you're saying about it not being possible.

I hope that made sense!

[Jess]

Thanks for your help!