The underlined word in ‘One truth of logic is the
validity of the so-called contrapositive, which says simply that if the statement…’ can be correctly classified
as a:
Opportunity Cost
This phenomenon goes by the name of ‘opportunity
cost,’ since by not investing in more equipment and
a more rigid production flow, the company is forgoing the opportunity to earn increased profits. These
costs are every bite as real as the payment of dollars
out-of-pocket.
This notion _______ opportunity cost can be reinforced _________ a famous saying ______ Benjamin
Franklin, no slouch himself _________ operations
management. To make the point, however, we must
make a brief excursion into logic. One truth of logic is
the validity of the so-called contrapositive, which says
simply that if the statement “If A, then B” is true, then
it is also true that “If not B, then not A.” That is, of every
time A occurs B follows, then we can be sure that if B
does not occur, then A did not occur as well. Enough
logic then, and back to Ben Franklin.
One of his Poor Richard sayings is that “A penny saved
is a penny earned.” We have all recognized the truth of
that since childhood, but I assert that by this saying
Ben showed us he knows everything about opportunity cost. After all, what is the contrapositive of “A
penny not earned is a penny not saved (i.e., a penny
sent). All we are saying by this notion of opportunity
cost is that “a penny not earned (an opportunity forgone) is a penny spent.” We shall often have occasion
to consider opportunity costs, in analyzing and deciding various operations issues.
SCHMENNER, Roger W. Production/Operations Management. 5th
Edition. Prentice-Hall, 1993.
Opportunity Cost
This phenomenon goes by the name of ‘opportunity cost,’ since by not investing in more equipment and a more rigid production flow, the company is forgoing the opportunity to earn increased profits. These costs are every bite as real as the payment of dollars out-of-pocket.
This notion _______ opportunity cost can be reinforced _________ a famous saying ______ Benjamin Franklin, no slouch himself _________ operations management. To make the point, however, we must make a brief excursion into logic. One truth of logic is the validity of the so-called contrapositive, which says simply that if the statement “If A, then B” is true, then it is also true that “If not B, then not A.” That is, of every time A occurs B follows, then we can be sure that if B does not occur, then A did not occur as well. Enough logic then, and back to Ben Franklin.
One of his Poor Richard sayings is that “A penny saved is a penny earned.” We have all recognized the truth of that since childhood, but I assert that by this saying Ben showed us he knows everything about opportunity cost. After all, what is the contrapositive of “A penny not earned is a penny not saved (i.e., a penny sent). All we are saying by this notion of opportunity cost is that “a penny not earned (an opportunity forgone) is a penny spent.” We shall often have occasion to consider opportunity costs, in analyzing and deciding various operations issues.
SCHMENNER, Roger W. Production/Operations Management. 5th
Edition. Prentice-Hall, 1993.
Gabarito comentado
Resposta correta: B — relative pronoun
Explicação central: a palavra which introduz uma oração que explica ou acrescenta informação sobre o substantivo anterior (“the validity of the so‑called contrapositive”). Esse é o papel clássico de um relative pronoun (pronome relativo).
Resumo teórico (progressivo): um pronome relativo liga duas orações e retoma um antecedente (ex.: who, which, that). Quando a oração relativa apenas acrescenta informação não essencial e vem entre vírgulas, fala‑se em non‑defining relative clause — e em inglês padrão essa função costuma ser desempenhada por which (para coisas) ou who (para pessoas). Fontes: Cambridge Dictionary / Oxford Learner’s.
Por que B está correta: aqui which retoma “the validity of the so‑called contrapositive” e atua como sujeito da oração relativa (“which says simply that…”). A vírgula antes indica que se trata de uma oração explicativa (non‑defining), reforçando a classificação como pronome relativo.
Análise das alternativas incorretas:
A — question word: palavras interrogativas (what, when, why) introduzem perguntas diretas ou indiretas; which pode ser question word em perguntas (“Which book?”) mas no exemplo funciona como ligador de orações, não como pergunta.
C — reflexive pronoun: pronomes reflexivos (myself, herself) referem‑se ao sujeito da mesma oração; which não tem essa função.
D — personal pronoun: pronomes pessoais (he, she, it) substituem nomes e não introduzem orações relativas; which não é personal pronoun.
E — possessive pronoun: (mine, yours) indicam posse; não se aplicam a which.
Dica prática para provas: identifique o antecedente e veja se há vírgula antes da palavra. Se a palavra liga duas orações e retoma um substantivo, pense em pronome relativo. Teste: retire a oração relativa — se a frase principal continuar completa, trata‑se de uma oração explicativa (non‑defining) normalmente iniciada por which.
Fontes rápidas: Cambridge Grammar of English; Cambridge Dictionary — entries on “relative clauses”.
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