By Valerie Adams
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Restriction Thus when two sets are related by a quantifier they have different roles. The first set establishes what entities we are talking about. It is known as the RESTRICTION set. The second set is the main predicate of the sentence. 14) 1 John was awake. 2 No students were awake. scope In both sentences the predicate is awake. In the first case the sentence can be translated into predicate notation as awake (John), as will be familiar from Chapter 3. The predicate awake has the same function in the second sentence, although this time it does not have an individual as its argument.
The denotation of ‘every’ was all the ordered pairs such that the first is a subset of the second. With ‘everybody’ we don’t have to worry about the restriction set—so the denotation is simply all the sets of which the set of people is a subset. a Give two examples of such sets which will be part of the denotation of ‘everybody’. b What will be the denotations of ‘somebody’ and ‘nobody’? Again, give two examples of the denotation of each. c You can now answer the question posed at the beginning of the chapter.
7), 1 is true if the individual tiny is a member of the set of alsatians, while 2 is true if he is a member of the set of dogs. To say that alsatian is a hyponym of dog is to say that the set of alsatians is a SUBSET of the set of dogs, so that it is impossible to be a member of the first without also being a member of the second. 8), in which A represents the set of alsatians, B the set of dogs, and the cross any random individual. 7) the predicate was a one-place relation (or property), so that its denotation was an ordinary set of individuals.
An Introduction to Modern English Word Formation by Valerie Adams