Reasoning

Logic and Fallacies

1,803 Questions

Understand the fundamentals of propositional logic, logical inference rules, and paradoxes. This set includes identifying logical fallacies, including those found in classical Nyaya logic. Strong grasp of these concepts is crucial for scoring well in the reasoning sections of competitive tests.

Propositional logic modelsLogical inference rulesTypes of logical fallaciesParadoxes and contingent truthsNyaya logic concepts

Logic and Fallacies Questions

Multiple choice

Directions: For this question, select the best of the answer choices given.

The more frequently employees take time to exercise during working hours each week, the fewer sick days they take. Even employees who exercise only once a week during working hours take less sick time than those who do not exercise. Therefore, if companies started fitness programs, the absentee rate in those companies would decrease significantly. Which of the following, if true, most seriously weakens the argument above?

  1. Employees who exercise during working hours occasionally fall asleep for short periods of time after they exercise.

  2. Employees who are frequently absent are the least likely to cooperate with or to join a corporate fitness program.

  3. Employees who exercise only once a week in their company's fitness program usually also exercise after work.

  4. Employees who exercise in their company's fitness program use their working time no more productively than those who do not exercise.

  5. Employees who exercise during working hours take slightly longer lunch breaks than employees who do not exercise.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The argument assumes that offering a fitness program will cause absent employees to participate and thus reduce absenteeism. Option B most seriously weakens this by showing that employees who are frequently absent are the least likely to join such programs, creating a selection bias that would make the program ineffective. If the people who most need the program won't use it, the absenteeism reduction won't happen. Options A, D, and E suggest minor side effects but don't undermine the core claim. Option C suggests supplementary exercise but doesn't weaken the main argument.

Multiple choice

An independent medical research team recently did a survey at a mountain retreat founded to help heavy smokers or cut down on their cigarette smoking. Eight percent of those persons smoking three packs a day or more were able to cut down to one pack a day after they began to try End-Smoke with its patented desire suppressant. Try End-Smoke to help you cut down significantly on your smoking. Which of the following could be offered as valid criticism of the above advertisement?

I. Heavy smokers may be physically as well as psychologically critically addicted to tobacco.II. A medicine that is effective for very heavy smokers may not be effective for the population of smokers generally. III. A survey conducted at a mountain retreat to aid smokers may yield different results than one would expect under other circumstance.

  1. I only

  2. II only

  3. III only

  4. II and III only

  5. I, II, and III
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(4) The ad is weak for two reasons. First, although it is addressed to smokers in general, the evidence it cites is restricted to heavy (three-packs-a-day) smokers. Second, the success achieved by the product was restricted to a highly specific and unusual location - the mountain retreat of a clinic with a population trying hard to quit smoking. Thus, II will undermine the appeal of the advertisement because it cites the first of the weaknesses. Ill also will tell against the ad since it mentions the second of these weaknesses. I, however, is irrelevant to the ad's appeal since the cause off a smoker's addiction plays no role in the claim of this ad to assist smokers in quitting or cutting down.

Multiple choice

Since 1990, the Japanese professional baseball league has permitted the use of a special bat made from a combination of wood and plastic. In each subsequent year, the Japanese league has reported fewer instances of bat breakage than has U.S. major league baseball. Based solely on this information, American team owners have enthusiastically reported to the Commissioner of American Baseball that the plastic-wood bats are more durable and break less easily than American all-wood bats. The conclusion drawn by the team owners assumes each of the following EXCEPT that

  1. the Japanese baseball season is not comprised of significantly fewer baseball games

  2. in both the U.S. and Japanese baseball leagues, batters are equally strong and pitchers throw equally fast

  3. the plastic-wood bat differs from all wood bats only in its durability, and would not otherwise significantly alter the game of baseball

  4. the reported instances of bat breakage in both the U.S. and Japanese baseball leagues accurately reflect the true ratio of Japanese-to-U.S. bat breakage

  5. since the Japanese league has permitted the use of the new bat, it has been used by a significant number of batters
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

(3) The Team Owners' CONCLUSION: The combination bats used in Japan are more durable than the all-wood bats used in America.THEIR EVIDENCE: For several years, Japanese baseball players have been allowed to use bats made of a combination of wood and plastic. Each season, there have been fewer reported instances of bats breaking in Japan than in America. The owners are generally assuming that the bats' composition, and not something else, accounts for the reduced breakage in Japan. Again we see cause and effect.(1) is an inherent assumption since fewer games will mean lesser usage. To qulify for acceptance, the modified bat has to last at least as long as the American season.  

Multiple choice

A formal system is a/an ___________________.

  1. Uninterpreted calculus

  2. Algebra

  3. Boolean algebra

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In logic and mathematics, a formal system consists of an abstract language and a set of inference rules. It is often referred to as an uninterpreted calculus because the symbols and rules are defined without reference to any specific meaning or 'interpretation.' Algebra is a specific type of formal system, but the general definition is an uninterpreted calculus.

Multiple choice

'The Vertical Velocity' is considered as one of the scariest rides in the world. In the last 30 years, there have been a few mishaps involving this ride, which resulted in a total of 6 deaths. People have been protesting for years that the ride should be shut down, but authorities seem to have ignored these protests and have decided to keep the ride open. In fact, they have reduced the admission tickets for the scary rides such as 'The vertical velocity'.

What if true, would explain the disinclination of the authorities to close down 'The Vertical Velocity'?

  1. The scare is more psychological than physical.

  2. As many as 60 thousand people have taken 'The Vertical Velocity' over the past 30 years.

  3. Similar other rides have witnessed higher fatality rates.

  4. Some of the deaths were due to cardiac arrest.

  5. The advisory boldly displayed at the site specifically forbids people with weak hearts to take the ride.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The argument does not mention the nature of mishaps and deaths. We don’t know whether the rides were directly and only because of the ride. Scary rides have thrill value. While some weak-hearted people are scared to take the ride, others look for such thrill. Those who are scarred need not take the ride, especially when the company specifically has put a notice.

Multiple choice

Some medical students avoid eating fried food. Therefore, some medical students are not overweight. I. Some medical students are underweight. II. People who eat less fried food are seldom overweight. III. Some medical students are cautious about their diets.

If the argument given above is true, which of the three statements should also be true?

  1. I and II

  2. II and III

  3. I, II and III

  4. III only

  5. II only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Correct answer. Statement II is validated by the use of 'therefore' before the conclusion. The argument is that they are not overweight because they don't eat fried food. This cause and effect relationship can be further extended. Statement III is inherent in the first sentence of the argument.

Multiple choice

Chocolates have been found to release a hormone in the human body that is responsible for happiness. Chocolates have also been found to be helpful in eliminating stress and work related fatigue. Therefore, the employees in IT sector should resort to eating chocolates while they are at work. This would boost up the performance and company’s profits significantly.

Which of the following assumptions is inherent in the argument?

  1. IT professionals don’t eat much of sugar which brings their performance down and results in a great loss to the employer too.

  2. Excess consumption of chocolates and the resultant high intake of sugar will not cause a decline in the performance of IT professionals.

  3. Since chocolate eating is said to add to performance levels, the cost will be borne by the company.

  4. The IT professionals are a stressed lot due to the nature of their work.

  5. The busy schedule of the IT professionals leaves them with spare time to savor chocolates.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Chocolate eating is said to relieve work related stress and is recommended specifically for IT professionals. So, the obvious assumption is that IT professionals face work related stress.

Multiple choice

The problems 3-SAT and 2-SAT are

  1. both in P

  2. both NP-complete

  3. NP-complete and in P respectively

  4. undecidable and NP-complete respectively
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

3-SAT is a classic NP-complete problem. 2-SAT can be solved in polynomial time (P) by converting it into an implication graph and checking for strongly connected components.

Multiple choice

The logic of pumping lemma is a good example of

  1. the Pigeon-hole principle

  2. the divide and conquer technique

  3. recursion

  4. iteration
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The pumping lemma relies on the fact that if a string is longer than the number of states in a DFA, the path must visit at least one state twice (the pigeonhole principle), creating a loop that can be repeated.

Multiple choice

Pseudo code is

  1. false logic

  2. programming aid

  3. both (1) and (2)

  4. neither (1) nor (2)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pseudocode is a high-level description of an algorithm that uses natural language constructs to help programmers plan the logic of a program before writing actual code.