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# DM - Grand Test -Q16

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+1 vote

Suppose S(n) is a predicate on natural numbers (Positive Integers), n and suppose

Now, if above assertion holds then Consider the following statements:

Which of the following is correct for above statements:

(A) Both Assertions Always holds

(B) Always holds but may or may not hold.

(C) may or may not hold but Always holds.

(D) Both can never hold. asked Aug 30, 2020
edited Sep 9, 2020

Suppose S(n) is a predicate on natural numbers (Positive Integers), n and suppose

\\ This says that If S(k) is true then S(k+2) is also true.

Now, if above assertion holds then Consider the following statements:

S1 is true when S(n) is true for all n. S1 is false when S(n) is true for all n > 9. So, S1 may or may not hold.

S2 is always true. If there exists some n for which S(n) is true then S(n+2) , S(n+4), S(n+6) and so on will also be true. So, If there exists some n for which S(n) is true then for infinite number of natural numbers S(n) will be true hence we can say that For all n there exists some m>n such that S(m) is true.

So, S2 always holds. answered Sep 9, 2020 by (226,240 points)