For each of the following, identify the premise and conclusion indicators, diagram the argument and supply any missing premises. (Exercises adapted from logic textbooks by Nolt, Hurley, Baronett, and Copi).



[1] One cannot doubt that the roof is sagging [2] and it has been leaking for many years. [3] It follows that, the roof will collapse soon.

Answer: “One cannot doubt that” (premise indicator), “it follows that” (conclusion indicator), 1 → 3 and 2 → 3


(1) [1] It is a fact that reduction of sodium may prevent hypertension in some people [2] and a high-salt diet is almost certainly not beneficial; [3] Accordingly, it is probably a good idea to reduce consumption of salty snacks.


(2) [1] Belief in spanking children implies that this practice is in some way essential to their proper upbringing; [2] I do not believe that it is essential to their proper upbringing; [3] for this reason I do not believe in spanking children.


(3) [1] Seeing that competent individuals are at liberty to make their own medical treatment decisions and [2] incompetent individuals are not, [3] as a result, competence and liberty are inextricably interwoven.


(4) [1] Legalizing marijuana for medical purposes would not contribute to the nation’s drug abuse problem. This is true because [2] the amounts involved would be small, and [3] the marijuana would be manufactured, stored and administered under strict security.


(5) [1] At one time Gary Kasparov had the highest ranking of any chess grandmaster in history. [2] However, he was beaten in a chess tournament by a computer program called Deep Blue, [3] so the computer program should be given a ranking higher than Kasparov.


(6) [1] Homework stifles the thrill of learning in the mind of the student. [2] It instills an oppressive learn-or-else disciple. [3] It quenches the desire for knowledge and the love of truth. [4] For these reasons homework should never be assigned.


(7) [1] We should never take our friends for granted. [2] True friends are there when we need them. [3] They suffer with us when we fail, and [4] they are happy when we succeed.


(8) [1] We are intelligent beings; [2] intelligent beings cannot have been formed by a crude, blind, insensible being: [3] there is certainly some difference between the ideas of Newton and the dung of a mule. [4] Newton’s intelligence, therefore, came from another intelligence.


(9) [1] There is a lot of pressure on untenured college teachers to dumb down their courses. [2] Administrators tend to rehire teachers who bring in more money, and [3] teachers who dumb down their classes do precisely this. Why? [4] Because easier classes attract more students and [5] more students means more money for the school.


(10) [1] Even if he [i.e., a Supreme Court nominee] were mediocre, there are a lot of mediocre judges and people and lawyers. [2] They are entitled to a little representation, aren't they, and a little chance? [3] We can't have all Brandeises and Frankfurters and Cardozos and stuff like that there. (Senator Roman Hruska of Nebraska, defending President Richard Nixon's attempt to appoint G. Harrold Carswell to the Supreme Court in 1970.)


(11) [1] Neither the butler nor the maid did it. [2] That leaves the chauffeur or the cook. [3] But the chauffeur was at the airport when the murder took place. [4] The cook is the only one without an alibi for his whereabouts. [5] Moreover, the heiress was poisoned. [6] It’s logical to conclude that the cook did it.