entailment questions and conditional statements Flashcards
(15 cards)
how to recognize entailment questions?
look for questions that ask you what must be true or for what logically follows sometimes the question ask you instead for what the conclusion would have to be if the statements in the stimulus are true
determine what else must be true based on those statements
entailment questions
if the statements above are true which one of the following must also be true?
Which one of the following logically follows from the statements above?
Which one of the following can be properly inferred from the statements above?
Entailment example
If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one’s musical roots.
If all of the statements above are true, which one of the following must also be true?
(A) If there are no sophisticated listeners in the audience, then there will be no inspired musical performances in the concert.
(B) No people who understand their musical roots will be in the audience if the audience will not be treated to a good show.
(C) If there will be people in the audience who understand their musical roots, then at least one musical performance in the concert will be inspired.
(D) The audience will be treated to a good show unless there are people in the audience who do not understand their musical roots.
(E) If there are sophisticated listeners in the audience, then there will be inspired musical performances in the concert.
Entailment example
If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one’s musical roots.
If all of the statements above are true, which one of the following must also be true?
How to approach this question
1) If there are any inspired musical performances in the concert, the audience will be treated to a good show, but
2) There will not be a good show unless there are sophisticated listeners in the audience, and
3) To be a sophisticated listener one must understand one’s musical roots.
✓ Look for ways that the passage’s statements interact and relate.
through symbolizing, we can investigate any potentially useful connections between good show statements and sophisticated listener statements.
✓ Identify conditional statements and consider symbolizing them.
Support often includes one or more conditional statements. These tend to be strong claims, and they are very useful for generating conclusions. It’s a good idea to notice conditionals wherever you come across them. If there are multiple conditions, and especially if they include common terms, it may be a good idea to symbolize them.
1) If there are any inspired musical performances in the concert, the audience will be treated to a good show.
inspired mus. perf. in concert → good show
2) There will not be a good show unless there are sophisticated listeners in the audience
good show → soph. listen.
3) To be a sophisticated listener one must understand one’s musical roots
soph. listen. → understand rootsHaving trouble understanding why we diagramed this unless statement this way?
Well, if the show can’t possibly be good unless there are sophisticated listeners in the audience, then it follows that if the show was good, then there must have been sophisticated listeners in the audience, right?
as you may be able to see, we can connect these statements! Notice how good show is the result of one statement and the trigger for another statement. The same is true of sophisticated listeners. That means that we can create one long chain of logic:
inspired mus. perf. in concert → good show → soph. listen. → understand roots
and the logically equivalent statement is
not understand roots → not soph. listen. → not good show → not inspired mus. perf. in concert
what is the contra positive of
A—–>B
-A——->-B
Contrapositive example
If I’m skateboarding, I will wear a helmet and protective gloves
if- sufficient
skateboarding ——> helmet and gloves
contra (we flip and negate every term)
no helmet and gloves ——> not skateboarding
*note If the term was positive before, then we make it negative. If it was negative before, we make it positive:
*pay attention to the word and (AND must be change to OR) if the original had OR it would change to AND
NOT HELMET OR NOT GLOVES—–> NOT SKATE BOARDING
Now we have a statement that is logically equivalent to the original statement! The original statement was that if I’m skateboarding, then I’m definitely wearing both helmet and gloves! So if I’m not wearing either of those two things, then I’m not skateboarding.
Main conclusion
-The claim that is backed by the rest of the argument as a whole
-Backed by support, but does not itself support any other claim
- The claim that the argument as a whole is trying to establish
sub conclusion
Also called intermediate or subsidiary conclusions
Claims that function as both conclusion and support
A conclusion that supports a further conclusion (or conclusions)
Backed by support, and simultaneously support a different claim
incorrect answer choices for main conclusion
-wrong element : includes statements from the stimulus that act as support, background and sub conclusions
-valid inferences : may state something that can be inferred from statements in the arguments but that isn’t the argument main conclusion
-not quite/ too strong : may be only slightly inaccurate misstatements of the main conclusion. For example, if the actual conclusion is that something is likely to be true, an incorrect choice may say that it is definitely true. This choice is incorrect because it’s stronger than the actual conclusion.
types of conclusions
comparison :This type of conclusion compares two elements with each other or compares one element with itself.
Examples
* It’s clear that this year’s candidate is stronger than last year’s candidate.
* It’s clear that this year’s candidate understands the public’s wishes better than she did a year ago.
**Top tip: Common indicators Comparative words (better than, healthier than, more useful than) can help you identify a conclusion as a comparison.
type of conclusions
causation : When one thing (such as an event, action, phenomenon) directly affects another, it’s a causal relationship.
Examples
-Last night, I took cough medicine and today I feel much better. So that cough medicine is really effective. (Cause: cough medicine; effect: feeling better)
-Jonathan gets good grades without trying very hard, and his teachers have said multiple times how much they like him. The only possible way that Jonathan maintains his good grades is because of how much his teachers like him. (Cause: teachers liking Jonathan; effect: good grades)
Top tip: Not so fast! If someone believes something to be true because of certain facts being true, that isn’t necessarily a causal relationship. Example: My friend always calls me on Wednesdays. Therefore, she’s definitely going to call me tomorrow. There is no direct cause and effect here because there isn’t something that is directly affecting something else.
type of conclusions
assessment
When an arguer assigns a certain subjective attribute to something, you might call it an assessment.
Examples
-The flower is beautiful.
-This policy is very helpful.
-The outcome will be important.
Note: Scientific facts aren’t assessments “The sun is made up of several gases” is a fact; “The sun is a joyful sight” is an assessment.
type of conclusions
recommendations
This type of conclusion asserts the best method or course of action (or, in its negative form, recommends against a certain method or course of action).
Examples
-In treating this disease, then, physicians should favor Treatment X.
-It’s likely that extending the warranty is the only way to gain new customers.
Top tip: look out for common indicators Often, a keyword such as “should” or “ought to” will signal a recommendation to you, but sometimes the recommendation is implied (such as in the example about the warranty).
type of conclusions Predictions
A prediction asserts the arguer’s opinion about something that will take place in the near or distant future.
Examples
-Obviously, the tennis match will be rescheduled.
-Our homeless population may not be reduced by next year.
Top tip for Identify the conclusion questions If the arguer believes something will or will not happen at some point in the future, the chances are good that it’s the argument’s main conclusion.
