Most successful entrepreneurs work at least 18 hours a day, and no one who works at least 18 hours a day has time for...

Naz January 3, 2014

Let's diagram:

"Most successful entrepreneurs work at least 18 hours a day,"

P1: SE-most-W@L18H
W@L18H-some-SE

"and no one who works at least 18 hours a day has time for leisure activities."

P2: W@L18H ==> not TLA
TLA ==> not W@L18H

"But all happy entrepreneurs have time for leisure activities."

P3: HE ==> TLA
not TLA ==> not HE

We are looking for the answer choice that CANNOT be true.

Let's diagram answer choice (D): HE-some-W@L18H

Well we know that if you are a happy entrepreneur, then you must have time for leisure activities. We also know that if you have time for leisure activities, you do not work at least 18 hours day.

HE ==> TLA ==> not W@L18H

Thus, through the transitive property, we can conclude: HE ==> not W@L18H.

So answer choice (D) cannot be true.

Hope that helped! Please let us know if you have any other questions.

TheFacu April 5, 2015

Can you diagram the answer choices please

Naz April 13, 2015

(A) Anyone who has no time for leisure activities works at least 18 hours a day.

So, we can rewrite this: "If you have no time for leisure activities, then you work at least 18 hours a day."

not TLA ==> W@L18H
not W@L18H ==> TLA

(B) Some entrepreneurs who work at least 18 hours a day are successful.

EW@L18H-some-S
S-some-EW@L18H

(C) Some happy entrepreneurs are successful.

HE-some-S
S-some-HE

(D) Some entrepreneurs who work at least 18 hours a day are happy

HE-some-W@L18H
W@L18H-some-HE

(E) Some successful entrepreneurs work less than 18 hours a day.

SE-some-not W@L18H
not W@L18H-some-SE

Hope that was helpful! Please let us know if you have any other questions.

yababio May 21, 2015

Video??????

Naz May 21, 2015

There is no need for a video explanation to this question since it has no major visual components. Please refer to the written explanation above for a breakdown of the problem.

Hope that helps! Please let us know if you have any other questions.

eskandarandrew May 14, 2018

if the passage states:

"and no one who works at least 18 hours a day has time for leisure activities."

P2: W@L18H ==> not TLA
TLA ==> not W@L18H

and

(A) Anyone who has no time for leisure activities works at least 18 hours a day.

So, we can rewrite this: "If you have no time for leisure activities, then you work at least 18 hours a day."

not TLA ==> W@L18H
not W@L18H ==> TLA

wouldn't this violate the "don't just reverse" premise of sufficient and necessary conditions?