In this problem, x + y + z > 0, and we are to determine if z > 1.
The problem is supposed to be rephrased to x + y < -1. But I don't understand why it isn't x + y > -1. If z is 3, for example, then x + y would need to be any number greater than - 3 for x + y + z to be > 0. But if x + y < -1, that wouldn't make x + y + z >0 if z >1.
What am I missing here?
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- RonPurewal
- Students
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- Joined: Tue Aug 14, 2007 8:23 am
Ah, yes, combining inequalities with other inequalities, how we love thee.
The first thing to keep in mind here is the fact that's in red ink on the slides: This statement is NOT equivalent to z > -1; it's a one-way inference. Specifically:
If x + y < -1, then z has to be > 1 to make up the difference (using exactly the same sort of reasoning you presented above). That's ALL that we're saying on the lab: if you have something SUFFICIENT to prove that x + y < -1, then you have something SUFFICIENT to prove the logical consequence that z > 1.
Note that the converse does NOT work. If x + y > -1, then z could have any value whatsoever (try picking some numbers if you don't see how this works).
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By the way, while your logic is correct, you're STARTING with z = 3 and drawing CONSEQUENCES from it. That's a bad idea, because DS problems work in the opposite way: you take the STATEMENTS (1) and (2) and draw consequences from THEM. The only time you should manipulate the prompt question is when you can come up with something EQUIVALENT to it.
The first thing to keep in mind here is the fact that's in red ink on the slides: This statement is NOT equivalent to z > -1; it's a one-way inference. Specifically:
If x + y < -1, then z has to be > 1 to make up the difference (using exactly the same sort of reasoning you presented above). That's ALL that we're saying on the lab: if you have something SUFFICIENT to prove that x + y < -1, then you have something SUFFICIENT to prove the logical consequence that z > 1.
Note that the converse does NOT work. If x + y > -1, then z could have any value whatsoever (try picking some numbers if you don't see how this works).
--
By the way, while your logic is correct, you're STARTING with z = 3 and drawing CONSEQUENCES from it. That's a bad idea, because DS problems work in the opposite way: you take the STATEMENTS (1) and (2) and draw consequences from THEM. The only time you should manipulate the prompt question is when you can come up with something EQUIVALENT to it.
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