1. Determine whether or not each of the following sentences is a proposition. Fo

Question

1. Determine whether or not each of the following sentences is a proposition. For each of those sentences that are propositions, write ts negation. In case the sentence is not a proposition, give a reason why it is not (a) "If whales are mammals then frogs are amphibians." (b) "I know what you did last summer." (c) The Dark Knight rises." (d) Tell me the time please." (e) This sentence is a proposition. (f) "The barber who shaves all men who do not shave themselves does not shave himself." (xx Marks)

Explanation / Answer

A sentence is a proposition if and only if it has a truth value either true or false.
   ex:4 is divisible by 2.   Truth value is "True"
       5 is divisible by 3.   Truth value is "False"

(a) answer:
   Given "If whales are mammals then frogs are amphibians"
  
   It is a proposition.
   NEGATION OF "If whales are mammals then frogs are amphibians" IS "whales are mammals and frogs are not amphibians"

(b)answer:
  
   Given "I know what you did last summer"
   It is not a propostion. Because we cannot give a truth value for this sentence.
(c)answer:
   Given "The Dark knights rises"
   It is not a propostion. Because it is not a really existing fact.So we cannot give truth value for this.

(d)asnwer:
   Given "Tell me the time please"
   It is not a propostion. Because this sentence is just a request.It is not a statement.
(e)asnwer:
   Given "This sentence is a proposition"
   Yes this sentence is a propostion because we can assign truth value for this sentence.
   NEGATION OF "This sentence is a proposition" IS "This sentence is not porpostion".

(f)answer:
   Given "The barber who shaves all men who do not shave themselves does not shave himself".
   It is propostion.NEGATION OF " "The barber who shaves all men who do not shave themselves does not shave himself" IS "The barber who shaves all men who do not shave themselves Shaves himself"

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