Subjective Type

Write cubes of all natural numbers between 1 and 20 and verify the following statement. If the statement is true then answer is 1 if not then the answer is 0 Statement: Cubes of all even natural numbers are even.

Solution

$$1 ^3 = 1 $$
$$2^3=8 $$
$$3^3=27$$
$$4^3=64$$
$$5^3=125 $$ so on.
Assume a general even number to be of the form $$2n $$ where $$n $$ is a whole number.
This is true for all even numbers, by definition are divisible by 2.
Cube of a general even number= $$2n \times 2n \times 2n =8n $$
This number $$8n$$ is again divisible by 2
So cube of an even natural number is even.

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