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Question
Give an example of a statement P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer
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Solution
P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true.
Let P(n) be 2n < n!
So, the examples of the given statements are,
P(0) ⇒ 20 < 0!
i.e 1 < 1 ⇒ not true.
P(1) ⇒ 21 < 1!
i.e 2 < 1 ⇒ not true.
P(2) ⇒ 22 < 2!
i.e 4 < 2 ⇒ not true.
P(3) ⇒ 23 < 3!
i.e 8 < 6 ⇒ not true.
P(4) ⇒ 24 < 4!
i.e 16 < 24 ⇒ true.
P(5) ⇒ 25 < 5!
i.e 32 < 60 ⇒ true, etc.
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