1 Propositions Problem 11 Consider the following statement \"For every nonnegati

Question

1 Propositions Problem 11 Consider the following statement "For every nonnegative integer, n, the value of n2 n +41 is prime." Is this a Proposition ? If so, is it atomic or molecular? Problem 1.2 Consider the following statement "Regenerating bits implies that although the bits will be repeated, there wil be no filtera Is this a Proposit ion ? If so, consider the following questions is it atomic or molecular ? Is this a TRUE or FALSE proposition? Problem 1.3 Consider the statement "If pigs could fly, then I will be king." From a discrete mathematics Point of view, is this logically truthful (valid)?

Explanation / Answer

Solution:-

A proposition is the basic building block of the logic. It can be defined as " A Declarative statement which is either true or false but not at the same time". The truth value for the proposition is either TRUE or FALSE.

For e.g. 1+ 1 = 2 it has a truth value TRUE.

1+ 1 = 5 it has a truth value FALSE

x < 5 it is not a proposition because it has not a truth value unique. It depends upon the value of x i.e. sometimes it may be true or sometimes it may be false (for e.g. if x is 2 its true and for x= 100 its false)

Now for the given statement in the above question we can say that

1. "For every nonnegative integer , the value of n2+n+41 is prime" is not a proposition because it has not a unique truth value.

Proof:- For n = 1 its value is 43 which is prime. Now just take another value of n = 41 the value is 1763 which is divisible by both 41, 43, 1 and 1763 hence its not prime. Hence it has both the truth value that depends upon value of n hence its proved that the given statement is not a proposition.

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