Math Is Fun Forum

rune2402

Banned

Registered: 2007-10-23

Posts: 32

valid or invalid

Determine whether the argument is valid or invalid.
Loretta's hobby is stamp collecting. If her husband likes to fish, then Loretta's hobby is not stamp collecting. If her husband does not like to fish, then Nathan likes to read. Therefore, Nathan likes to read.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: valid or invalid

Let's introduce some pronumerals to make things simpler.
p = Loretta's hobby is stamp collecting.
q = Her husband likes to fish.
r = Nathan likes to read.
Then the statements read:

   ...[1]

   ...[2]

We know p is true. By taking the contrapositive of [1], we have:

  ...[3] (hmm...)

Combining [2] and [3] using the law of transitivity, we have:

Therefore, the argument is valid.

Last edited by Identity (2007-10-30 18:38:29)

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: valid or invalid

Oh my god. I am learning more here than in school. Thanks so much i have a test in the mornin.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: valid or invalid

Actually, I'm not 100% about my use of the contrapositive...

While it's true that if

then

I'm worried that this might not work if you have negate b:

then

soz, you could try looking up the properties of the contrapositive

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: valid or invalid

For the contrapositive of q then p :

not q then not p

Last edited by rune2402 (2007-10-30 18:48:51)

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: valid or invalid

I have to regroup tomorrow on this. I'll study transitivity and back here.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: valid or invalid

This one is killing me because I really do not understand the law of transitivity or how it relates to the validity of an argument. I'll be studying this in depth. I'll be back.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: valid or invalid

I'm worried that this might not work if you have negate b:

then

That is perfectly fine. It works.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: valid or invalid

I am totally lost. it appears this question was the only one in my book section that i completely do not munderstand. I still o not know mif it is valid or not. I will have to regroup on this one.

You are a genius.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: valid or invalid

I'm worried that this might not work if you have negate b:

then

That is perfectly fine. It works.

Yeah what she said. If you want to be really rigorous, you could include an intermediate step in there of

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Why did the vector cross the road?
It wanted to be normal.