Name: 1) (10 points) Select the best answer for each of the following. By defini

Question

Name: 1) (10 points) Select the best answer for each of the following. By definition, a set is countable if it is: (a) finite (b) infinite (c) countably infinite (d) all of the above (e) either (a) or (c) By definition, a bijection is (a) one-to-one (b) a total function (c) onto (d) all of the above (e) none of the above A language is: (a) a finite set of symbols (b) a set of strings (c) a set of states (d) always regular (e) none of the above All languages are: (a) regular (b) finite (c) infinite (d) based on the alphabet (0, 13 (e) none of the above By definition, a set is countably infinite if it: (a) is infinite (b) has the same cardinality as the set N of natural numbers (c) consists only of integers (d) all of the above (e) none of the above

Explanation / Answer

By definition, a set is countable if it is finite or countably infinite so the answer is (e) By definition,a bijection is one-to-one,onto and a total function so answer is (d) A language is a set of strings so answer is (b) All languages are finite so answer is (b) By definition ,a set is countably infinite if it is infinite so answer is (a)

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