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Properties of Iota

If n is odd...

Question

If $n$ is odd , then $n^{3}$ is also odd.

A

True

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B

False

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Solution

The correct option is A True
Let $n = 3$
$∴ n^{3} = 3 \times 3 \times 3 = 27$
$∴$ If n is odd, $n^{3}$ is also odd is a true statement.

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Similar questions

Q. By taking three different values of n verify the truth of the following statements:
(i) If n is even , then n³ is also even.
(ii) If n is odd, then n³ is also odd.
(iii) If n leaves remainder 1 when divided by 3, then n³ also leaves 1 as remainder when divided by 3.
(iv) If a natural number n is of the form 3p + 2 then n³ also a number of the same type.

Q. If n is an odd integer greater than or equal to 1 then the value of

n^{3} - {(n - 1)}^{3} + {(n - 2)}^{3} - . . . + {(- 1)}^{n - 1} {.1}^{3}

n

is an odd integer greater than or equal to

1

, then the value of

n^{3} - (n - 1)^{3} + (n - 2)^{3} - . . . . + (- 1)^{n - 1} 1^{3}

Q. Consider the statement

:

^{''}

n

n^{3} - 1

n

^{''}

. The contrapositive statement of this statement is :

n

n^{3}

is also even. Enter

1

if statement is true or enter

0

is the statement is false.

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