ASSIGNMENT 1
See questions here.
Contents:
The man saw the woman with a telescope.
Man has the telescope:
The man with a telescope saw the woman.
Woman has the telescope:
The woman with a telescope was seen by the man.
Sisters reunited after ten years in checkout line at Safeway.
Sisters reunited in checkout line at Safeway after ten years.
Large hole appears in High Street. City authorities are looking into it.
City authorities are looking into the appearance of a large hole in High Street.
Mayor says bus passengers should be belted.
Mayor says bus passengers should wear seatbelts.
No head injury is too trivial to ignore.
The alternative meaning that can be drawn is: the lack of head injury is too trivial to ignore, implying that the lack of head injury must be looked into due to its triviality. A reformulation to make the intended meaning clear:
A head injury is never too trivial to ignore.
In case of fire, do not use elevator.
The first meaning is: if a fire occurs, do not use the elevator. The second meaning is: do not use the elevator, since a fire may occur (this implies a preventative measure rather than a measure to be taken in the case of an actual fire). The meanings are based on the two ways “in case” can be used: in the first way, “in case” means “if”, in the second way, “in case” means “given the chance that”. A reformulation to make the intended meaning clear:
If fire occurs, do not use elevator.
The statement “This page is left intentionally blank” conveys to the reader that the page is intentionally left devoid of information relevant to the purpose of the document; hence, “blank” here does not mean literally blank, only blank with respect to relevant information. “Blank” here could also refer not to the page as a whole but to the page apart from this printed statement. However, logically, given the meaning of “blank” and given the fact that the page is referred to as a whole, the statement is self-contradictory, since it being printed on a page makes the page no longer blank. Two reformulations of this statement to avoid such a logical problem:
1.
The rest of this page is intentionally left blank.
2.
This page intentionally lacks information relevant to the document’s purpose.
The temperature is hot today.
“Hot” is an adjective that describes the relative temperature of an object or substance. Hence, temperature, which is an attribute of which “hot” is a measure, cannot itself be hot. Hence, the given statement is logically invalid. However, to reformulate the statement to convey the intended meaning:
To show that not every number of the form $N = p_1 p_2 … p_n + 1$ is a prime (given that $p_1, p_2 … p_n$ are all primes), we only need to show one example of such a number that is not prime.