Formal Logic
Formulate the contrapositive:
If Alicia is not home -> Jenn visits Beatriz OR Carmela
If Jenn does not visit Beatriz AND does not visit Carmela -> Alicia is home
To formulate the contrapositive of a conditional statement, reverse the order of its clauses and negate each clause.
Five horses - A, B, C, D, and E - will begin a race behind gates numbered 1 through 5. Each gate has exactly one horse behind it. The following conditions apply:
There are exactly two gates between the starting position of A and D.
C starts at gate 2.
Draw an appropriate sketch.
A/D in gate 1
C in gate 2
N/A in gate 3
A/D in gate 4
N/A in gate 5
The spread of Protestantism in Europe had several effects, including...But its most notable effect was...
Which of the two redacted portions of this excerpt is more likely to be the basis for the LSAT questions
The second portion
While the first portion may include details relevant to answering questions, the contrast word "but" and the emphasis words "most notable" indicate the location of facts the author thinks are most important
Because of her high volume sales in the past few months, Wanda will certainly win the salesperson of the quarter award.
Identify the conclusion of the above argument
Conclusion: Wanda will win the award.
"Because" introduces the evidence (the high volume of sales) offered to support a prediction about Wanda.
Identify the sufficient condition and the necessary condition in the following statement.
If Dorian stops for coffee, she will be late for class
Sufficient condition: Dorian's stopping for coffee
Necessary condition: Dorian's being late to class
Getting coffee is sufficient to guarantee that Dorian will be late; being late is a necessary result of stopping for coffee
Translate the following rules into shorthand:
No more than two people work on any given day.
Alan does not work earlier in the week than Carolyn.
Never A...C
The second rule should not be interpreted as C...A. The first rule implies two people can work on the same day, so C and A could be together.
For example, one of the first albums to feature the Moog synthesizer was Wendy Carlos's Switched-On Bach, on which the artist interpreted the music of Johann Sebastian Bach
Where in the passage would you find the point that this example is intended to support?
In the sentence immediately preceding this example
Examples help to illustrate or clarify points made by the author of the passage. They are tested in questions that ask how the author supports a claim or why the author included the example's details.
Town X will experience severe property damage, next week, as recent weather forecasts show a chance that a hurricane will strike the town then.
Identify the assumption(s) in this argument.
Assumption: The hurricane will strike the town and cause severe damage.
The author makes a leap from the evidence that an event MAY happen to a prediction that it WILL happen and, furthermore, equates the arrival of the hurricane with the infliction of severe damage.
Identify the sufficient conditions and the necessary conditions in the following statement.
Unless it rains, Ramona will go on a bike ride.
Sufficient condition: that it's not raining or that Ramona does not go on a bike ride
Necessary condition: Ramona's going on a bike ride or that it's raining
The original statement can be rewritten as: "If it does not rain then Ramona will go bicycling" or "If Ramona did not go on a bicycle ride, then it is raining"
Translate the following rule into shorthand given that each performance features exactly one performer:
L cannot perform before K unless L performs first.
If L...K -> L =1st
If L ≠ 1st -> K...L
The term "unless" signals a conditional statement indicating that any time L is not in the first position, K must precede L in the sequence.
Despite some concerns about the adequacy of the questions posed in them, consumer confidence surveys offer the best indicator of a nation's economy.
Based on the excerpt, what is the author's attitude toward consumer confidence surveys?
Approval
The author acknowledges concerns with the survey's methodology, but still asserts that they are the best available economic indicator.
Corporation X must be a profitable business. If it weren't, it would not be able to survive despite expenses that consistently outpace revenue.
Identify the flaw in this argument.
The evidence contradicts the conclusion.
Having expenses that exceed revenue is the definition of being unprofitable, but the argument uses this information to support the conclusion that the business is profitable.
Translate the following conditional statement, and its contrapositive, into "if/then" shorthand.
Aparna will pass her class only if she hands her paper in on time.
If passes -> paper on time
If paper not on time -> does not pass
To translate a statement into Formal Logic shorthand, place the terms in the sufficient clause after the "If" and the terms in the necessary clause after the arrow indicating "then". To formulate the contrapositive, reverse and negate the terms.
Six movies are each shown on exactly one of two days, Monday or Tuesday.
No more than 4 movies will be shown on Monday.
What is the minimum number of movies that could be shown on Tuesday?
2
If the maximum of four movies are shown on Monday, the remaining two will be shown on Tuesday. Any fewer movies on Monday would mean more movies on Tuesday.
Though some environmentalists have concerns about how effective this plan will be, it appears to be the only chance to save the species.
Based on this excerpt, what is the author's attitude toward the plan?
Approval
With the contrast word "though", the author indicates her belief that the dire consequences of not trying the plan (a specie's extinction) overrides the environmentalist's concerns.
The current deck does not meet local building codes. While the deck satisfied codes when it was built, the current owners should have brought it up to code before trying to sell the home.
What principle about code violations would justify the recommendation?
Homeowners should fix any code violations before trying to sell their home, even if they didn't initially violate the housing code.
If A AND B -> X AND Y
If X happens but Y does not, what do you know about A and B?
At least one of A or B does not happen.
If A and B both happen, then both X and Y must happen as well. Since Y did not happen, then it cannot be the case that both A and B have happened. Either only one of them happened or neither did.
Translate the following rule into shorthand:
Denise watches fewer movies than Neal does.
D < N
Thus, it is critical to continue to emphasize the value of education in early childhood development.
What is the function of this excerpt?
Author's conclusion
"Thus" indicates that this sentence is a conclusion; the evidence for it precedes the excerpt in the passage. Note the word "critical" indicates this idea is important to the author.
Only children under 48 inches tall are allowed in the designated play area. Traci is 50 inches tall.
Based on the statement above, what must be true about Traci?
Traci is not allowed to play in the designated area