Question 12 Marks
If P(n) is the statement "n3 + n is divisible by 3", prove that P(3) is true but P(4) is not true.
Answer
View full question & answer→P(n): n3 + n is divisible by 3
P(3): 33 + 3 is divisible by 3
⇒ P(3): 30 is divisible by 3
$\therefore$ P(3) is true.
Now,
P(4): 43 + 3 = 67 is divisible by 3
Since, 67 is not divisible by 3
So, P(4) is not true.
P(3): 33 + 3 is divisible by 3
⇒ P(3): 30 is divisible by 3
$\therefore$ P(3) is true.
Now,
P(4): 43 + 3 = 67 is divisible by 3
Since, 67 is not divisible by 3
So, P(4) is not true.