If the price it pays for coffee beans continues to increase, the Coffee Shoppe will have to increase its prices. In t...

on July 31 at 10:41PM

s/n condition diagram please

I answered with B. Can you explain please?

2 Replies

Irina on August 1 at 06:03PM

@yoyo,

Let's diagram this argument:

IF the coffee bean price continues to increase (P) THEN increase prices (Q)

P->Q

(IF increase prices) THEN sell noncoffee (R) or sales will decrease (S)

Q-> R v S

IF sell noncoffee (R) THEN decrease profitability (T)

R->T

IF NO decrease in profitability (~T) THEN sales do not decrease (~S)

~T-> ~S

Now, let's put all the premises together and see what inferences can we make. Rules of inference used are on the side:

(1) P -> Q
(2) Q -> R v S
(3) R -> T
(4) ~T -> ~S
___________
(5) P -> R v S (hypothethical syllogism (1) & (2))
(6) S ->T (transposition (4))
(7) R v S -> T (composition (3)(6))
(8) P -> T (hypothetical syllogism (5) & (7))

Therefore, IF the price of coffee beans (P) continues to increase, THEN profitability (T) continues to decrease as expressed in the correct answer choice (C).

There are many ways we could reach the same conclusion of course - let's try another deduction tree to check our logic. Note this is only to further illustrate formal logic rules, it is not something I would do on a real test.

Option 2

(1) P -> Q
(2) Q -> R v S
(3) R -> T
(4) ~T -> ~S
_____________
(5) P -> R v S (hypothetical syllogism (1) & (2))
(6) ~ T -> ~R (transposition (3))
(7) ~T -> ~R ^ ~S (composition (4) (6))
(8) R v S -> T (De Morgan's Theorem (7))
(9) P -> T (hypothetical syllogism (5) (8))

Let me know if this helps and if you have any other questions.

Ravi on August 1 at 07:21PM

@yoyo33,

Let's take a look at (B) and (C).

(B) says, "If the Coffee Shoppe’s overall profitability decreases,
either it will have begun selling noncoffee products or its coffee
sales will have decreased."

Both of these things would decrease the Shoppe's profitability (as
mentioned in the stimulus), but it's possible that other things could
have the same effect, such as people substituting smoothies for
coffee, or something like that. (B) is incorrect because it's
confusing sufficient conditions for necessary conditions. These
conditions are mentioned as sufficient in the stimulus to decrease the
Shoppe's profitability, but this answer choice paints at least one of
them as a necessary condition. Thus, (B) is out.

(C) says, "The Coffee Shoppe’s overall profitability will decrease if
the price it pays for coffee beans continues to increase."

(C) is great, as it's the conclusion that we arrive at from combining
all of the premises together.

Price it pays for coffee beans continues to increase - >shoppe
increases its prices - >sell noncoffee products OR sales decrease

sell noncoffee products - >decrease shoppe's profitability

sales decrease - >decrease in profitability for the shoppe

If the price it pays for coffee beans keeps on increasing, the Coffee
Shoppe is bound to see a decrease in overall profitability.

Does this make sense? Let us know if you have any other questions!