Question 11 Mark
Justify: Let P(n) be a statement and let P(k) ⇒ P(k + 1), for some natural number k, then P(n) is true for all n ∈ N.
Answer
View full question & answer→False.
Solution:
Given that,
P(k) ⇒ P(k + 1) for some natural number k
P(1) ⇒ P(2) but if $\text{P}(2)\nRightarrow\text{P}(3)$ [or $\text{P(k)}\nRightarrow\text{P(k+1)}$ for some k]
Then P(n) will not be true for all n ∈ N.
Hence, the statement is 'False'.
Solution:
Given that,
P(k) ⇒ P(k + 1) for some natural number k
P(1) ⇒ P(2) but if $\text{P}(2)\nRightarrow\text{P}(3)$ [or $\text{P(k)}\nRightarrow\text{P(k+1)}$ for some k]
Then P(n) will not be true for all n ∈ N.
Hence, the statement is 'False'.