# logic

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What would be the standard form of the following sentence?

"The only road to success is hard work"

So now I'm thinking: "All things that are members of the class of which the road to success is the only member are hard work."

What is correct?

• logic -

The first sentence is grammatically correct. However, success is sometimes a surprise and just happens... a fluke of fate. So logically that is not an accurate statement.

The logical statement would be "Most roads to success require hard work."

• logic -

Logically speaking, if the only road to success is hard work, then if one goes the road of hard work, it may lead to success, since there may be diversions off that road.

so, all members of success include hard work, but all results of hard work is not success.

On a Venn Diagram, the set of success would be a subset of hard work, but there are other subsets of hard work.

• logic -

or Success is a subset of hard work.

• logic -

If successful, then worked hard.

• logic -

Statement - If cow, then mammal- assume true
converse - If mammal, then cow - maybe
inverse - if not cow, then not mammal - maybe
contrapositive - if not mammal, the not cow - true

In this case:
Statement - If successful - then worked hard
converse - if worked hard, then successful - maybe
inverse - if not successful, then did not work hard - maybe
contrapositive - If did not work hard, then not successful - true

• logic -

I just want to know the correct standard form of the original sentence.

• logic -

This sentence would be correct.

"Most roads to success require hard work."

• logic -

Guru - but the original statement "requires" hard work (if and only if).
It is a formal logic question.

• logic -

You have hard work as a subset of success.
(allowing for success some other way)
But success is a subset of hard work.
(only via the hard work road)

• logic -

If you are successful, you took the hard work road.

• logic -

I am SOOOO glad I don't teach this stuff. Way too picky!

• logic -

It is not hard to get the logic right if you draw a Venn diagram as bobpursley suggested.
The success circle is inside the hard work circle from the original sentence:
"The only road to success is hard work"

You absolutely have to be somewhere in that hard work circle to get in the little success circle :)

• logic -

Venn diagram or no, the statement:

"The only road to success is hard work"

is grammatically correct but logically incorrect. Some people achieve success without travelling the path of "hard work", which is a metaphor anyway.

• logic -

Who ever said logic had to be logical ? :)

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