Help with Transitive Property Question Forum

[dadownclub8]

Hi. I'm a bit confused on this question especially with how the transitive property works here.

I diagrammed the stimulus as follows:

HS->WO and SM
WK->HS
SM->(NOT RC)

I understand I can put premise two on top of premise one.

So it would look like this.

WK->HS
HS->WO and SM
SM->(NOT RC)
Therefore: WK->(NOT RC)

My question is this: for premises two and three I see that the SM is in common however, I don't understand how it connects because don't you need both WO and SM to connect? Shouldn't premise three be WO and SM->(NOT RC) for the connection to happen and not just the term SM? I apologize if this is a rather stupid question but it's been bugging me.

[CardozoLaw09]

Hi. I'm a bit confused on this question especially with how the transitive property works here.

I diagrammed the stimulus as follows:

HS->WO and SM
WK->HS
SM->(NOT RC)

I understand I can put premise two on top of premise one.

So it would look like this.

WK->HS
HS->WO and SM
SM->(NOT RC)
Therefore: WK->(NOT RC)

My question is this: for premises two and three I see that the SM is in common however, I don't understand how it connects because don't you need both WO and SM to connect? Shouldn't premise three be WO and SM->(NOT RC) for the connection to happen and not just the term SM? I apologize if this is a rather stupid question but it's been bugging me.

No you don't need WO as well as SM to get NOT RC. SM on its own is sufficient to trigger NOT RC, so whenever you have SM, which is what you get whenever you have HS, then you also trigger NOT RC in the process; the transitive property is perfectly applicable to this Q.

[dadownclub8]

Sorry I'm still confused. Why wouldn't you need both terms for the transitive to follow?

[ScottRiqui]

Sorry I'm still confused. Why wouldn't you need both terms for the transitive to follow?

The single statement HS->WO and SM is equivalent to the two individual statements HS->WO, HS->SM.

So HS gives you SM, and SM gives you NOT RC. The fact that HS also gives you WO isn't needed.

[CardozoLaw09]

Sorry I'm still confused. Why wouldn't you need both terms for the transitive to follow?

The transitive property is if A ---> B and B --->C, then A ---> C. Similarly,
(1) WK ---> HS
(2) HS ---> WO and SM
(3) SM ---> NOT RC
Therefore WK --> NOT RC

What's troubling you is the WO but that term is inconsequential in this case because HS triggers BOTH WO and SM, and whenever SM is triggered then NOT RC is the result. Also, it might be more helpful if you mentioned what PT/question this is.

[dadownclub8]

My apologies. Should have specified. It's PT 40 June 2003 Sec 1 #22

[ScottRiqui]

My apologies. Should have specified. It's PT 40 June 2003 Sec 1 #22

C must be true. The fact that they're well-known means that they're highly successful. The fact that they're highly successful means that they're self-motivated (along with being well-organized, although that doesn't matter for this), and since they're self-motivated, they don't regret their career choice.

[CardozoLaw09]

You guys should take down the question (TLS copyright policy) and just leave the PT, Section, and Question number

[dadownclub8]

Thanks for the help.

Just to clarify to make sure that I understand the property clearly.

So if A->B
B-> C and D
D->E

it follows that A->E since premise 2 can be split up as B->C and B->D and the second of these would trigger premise 3.

Both C and D may be necessary for B to occur however for the purposes of the transitive property are irrelevant.

[CardozoLaw09]

Thanks for the help.

Just to clarify to make sure that I understand the property clearly.

So if A->B
B-> C and D
D->E

it follows that A->E since premise 2 can be split up as B->C and B->D and the second of these would trigger premise 3.

Both C and D may be necessary for B to occur however for the purposes of the transitive property are irrelevant.

Yes

[ScottRiqui]

Both C and D may be necessary for B to occur however for the purposes of the transitive property are irrelevant.

Yes, both C and D *will* have to be true for B to be true. The contrapositive of

B-> C AND D

is

NOT C OR NOT D -> NOT B

So if either (or both) of C or D is missing/not true, then B can't be true.

When you're negating statements that have terms separated by AND or OR, the AND gets changed to OR, and vice-versa. I think it's DeMorgan's theorem, but don't hold me to that. Here's another example:

Statement: X-> Y OR Z

Contrapositive: NOT Y AND NOT Z -> NOT X

[dadownclub8]

Thanks for the replies and the help!