Only if the electorate is moral and intelligent will a democracy funct

Question

Only if the electorate is moral and intelligent will a democracy function well.

Which one of the following can be logically inferred from the claim above?

(A) If the electorate is moral and intelligent, then a democracy will function well.

(B) Either a democracy does not function well or else the electorate is not moral or not intelligent.

(C) If the electorate is not moral or not intelligent, then a democracy will not function well.

(D) If a democracy does not function well, then the electorate is not moral or not intelligent.

(E) It cannot, at the same time, be true that the electorate is moral and intelligent and that a democracy will not function well.

I have marked D as the ans considering the correlation provided is A > B, then ~B > ~. Can somebody please respond>?

ponderer · Accepted Answer

This is not a 700-level question.
It is a basic logic structure - I'll explain generally:

Only if x, then y.

This tells you, from x conditional:
1) If x does happen, y may or may not happen.
2) If x does not happen, y does not happen.

Same two, from y conditional:
3) If y does happen, then x happens.
4) If y does not happen, then x may or may not happen.

Now go over answers.

cano · Answer

Try to rewrite the sentence in a different order:
A democracy will function well only if the electorate is moral and intelligent.
Conclusions:
1. Electorate not moral or not intelligent: democracy will not function well.
2. Electorate is moral and intelligent: democracy may function well (could function well, could not function well).
3. Democracy will not function well: electorate is moral and intelligent or electorate is not moral and intelligent.

A. Not necessarily, see 2.
B. No, the democracy may not function well with an intelligent and moral electorate, see 2.
C. This is right, see 1.
D. Not only, it could be that the electorate is moral and intelligent, see 2.
E. Yes, it could, see 3.

I hope it helps. If so, consider awarding with kudos.

seekmba · Answer

this is a pure mathematical logic question

If A is true, then B must be true (A implies B)

If A then B
so
If not B then not A (True)

We have to find a statement that stands true to (if not B then not A)

The question says

Only if the electorate is moral and intelligent will a democracy function well.

the catch here is the word "Only"

so the sentence can be rewritten as:

Democracy will function well (D) Only when the electorate is moral and intelligent (M)

D ==> M

We have to find (Not M then Not D)....only C stands true to this relationship.

C says If the electorate is not moral or not intelligent (not M), then a democracy will not function well (not D).

If no morality then no democracy

dwivedys · Answer

GMAT hardly tests these kinds of questions. But I think it should be E. The original premise has an AND between morality and intelligence (moral AND intelligent). The answer choices use OR (not moral or not intelligent). Not moral or not intelligent could mean Not moral but intelligent OR moral but not intelligent. So this breaks the original premise IMO. E stands true regardless - it cannot AT THE SAME TIME be true that an electorate is moral and intelligent and democracy does not function well.

Testluv · Answer

Hi

dwivedys is correct--this is not a GMAT-like question.

It is an LSAT or LSAT-like question testing technical formal logic skills in a way that GMAT never would.

We have:

"Only if" tells us that the electorate's being moral and intelligent are necessary conditions for a well-functioning democracy.

Because they are necessary for a well-functioning democracy, if we don't have either of them, then we won't have a well-functioning democracy. This is what choice C says. Thus, choice C can be properly inferred.

We can't infer choice A because we only know that the electorate's being moral and intelligent are necessary conditions for a well-functioning democracy--we don't know that they are sufficient--we don't know that they will guarantee a well-functioning democracy. For the same reason, we can't infer choice E.

We can't infer choice D because there may be many other reasons why a democracy is not functioning well.

---

Here's an analogy:

Only if you have a gas tank and a functioning batter will you be able to drive your car.

We can infer that if you don't have a gas tank or if you don't have a functioning battery then you won't be able to drive your car. This inference is analgous to choice C of this question.

Can we infer that if your car isn't driveable it's because there is no gas tank or because the battery isn't functioning? Of course not, there may be other reasons your car isn't driveable. So, this improper inference is like choice D of this question.

Can we infer that if you do have a gas tank and a functioning battery, you will certainly be able to drive your car? Of course not, because your car may not have tires! So, this improper inference is like Choices A and E of this question.

YangYichen · Answer

Only if the electorate is moral and intelligent will a democracy function well.
Which one of the following can be logically inferred from the claim above?
(A) If the electorate is moral and intelligent, then a democracy will function well.
(B) Either a democracy does not function well or else the electorate is not moral or not intelligent.
(C) If the electorate is not moral or not intelligent, then a democracy will not function well.
(D) If a democracy does not function well, then the electorate is not moral or not intelligent.
(E) It cannot, at the same time, be true that the electorate is moral and intelligent and that a democracy will not function well.

I understand why C is right but don't understand why D is wrong

sayantanc2k · Answer

I do not see any problem with D. 
IF (A and B) THEN C
from above it can be deduced:
IF (NOT C) THEN (NOT(A AND B))
i.e.,
IF (NOT C) THEN ((NOT A) OR (NOT B))..................<NOT(A AND B) = (NOT A) OR (NOT B)>
Thus D should also be alright.

Drb89 · Answer

I have found a quite easy trick to solve this type of questions (If A, then B)

Approach this question type with Boolean "AND" operation. So there are several inputs, A1, A2, A3, etc. to give output

So for our answer to be True, all inputs need to be True

Even if one input is False, then output is False. Also, it doesnt mean since A1 is true, our output will also be True. So every statement must be True

Option C says that, one input is False. so we know that output will be False, no matter what other inputs are.

totamofficiis · Answer

it is a basic logic question and i believe the reasoning is wrong.
only if : x -> y means it is one to one. for this logic i can write x-->y and y-->x there is an and operation there so a^b -> y meaning not y -> not a or not b; because of only if not a or not b also implies y. hence 2 answers are correct. If we are treating only if as if. then option d is correct. as x->y then not y -> not x. we can never infer from x->y to not x -> not y. so it is mathematically not correct.

jainendradubey · Answer

This is a perfect example of the question type necessary vs sufficiecny where only if x happens will y happen makes x necessary but not sufficient for y to happen.

Rishab2409 · Answer

Hi, I understand this is from Conditional Reasoning topic. The question stem says ”Only if Y, then X” should the answer not contain ‘If X, then Y’, if yes then the correct answer will be A, please guide.

guddo · Answer

Only if the electorate is moral and intelligent will a democracy function well. 
 
Which one of the following can be logically inferred from the claim above?

“Only if” introduces a necessary condition. So the statement means: if a democracy functions well, then the electorate must be moral and intelligent.  The valid inference is the contrapositive : if the electorate is not moral or not intelligent, then the democracy will  not  function well.

(A) If the electorate is moral and intelligent, then a democracy will function well.

Wrong. This reverses the logic. Moral and intelligent electorate is necessary, not sufficient.

(B) Either a democracy does not function well or else the electorate is not moral or not intelligent.

Wrong. This says a well-functioning democracy and a moral, intelligent electorate cannot both exist. That is the opposite of the original logic.

(C) If the electorate is not moral or not intelligent, then a democracy will not function well.

Correct. This is the contrapositive of the original statement.

(D) If a democracy does not function well, then the electorate is not moral or not intelligent.

Wrong. This negates both sides. A democracy might fail for other reasons even if the electorate is moral and intelligent.

(E) It cannot, at the same time, be true that the electorate is moral and intelligent and that a democracy will not function well.

Wrong. The original statement does not say a moral and intelligent electorate guarantees a well-functioning democracy.

Answer: (C)

guddo · Answer

You are right about the rule, but the symbols are reversed.

“Only if Y, then X” really means:

If X, then Y.

Here:

X = democracy functions well
 Y = electorate is moral and intelligent

So the statement means:

If democracy functions well, then the electorate is moral and intelligent.

A says the reverse:  If Y, then X . That is not guaranteed.

C is correct because it gives the  contrapositive : if not Y, then not X.

Only if the electorate is moral and intelligent will a democracy funct

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Only if the electorate is moral and intelligent will a democracy funct

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