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Prove by direct method that for any inte...

Prove by direct method that for any integer n, `n^(3)-n` is always even.

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Hence the given statement is proved.
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KUMAR PRAKASHAN-MATHEMATICAL REASONING-SOLUTION OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. Write down the converse of following statements: If x:y=3:2 then 2x=...

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  2. Write down the converse of following statements: If S is a cyclic qu...

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  3. Write down the converse of following statements: If x is zero then x...

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  4. Write down the converse of following statements: If two triangles ar...

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  5. Identify the Quantifiers in the following statements: There exists a...

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  6. Identify the Quantifiers in the following statements: for all real n...

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  7. Identify the Quantifiers in the following statements: There exists a ...

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  8. Identify the Quantifiers in the following statements: For every natur...

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  9. Identify the Quantifiers in the following statements: For all real n...

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  10. Identify the Quantifiers in the following statements: There exists a...

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  11. Identify the Quantifiers in the following statements: for all negativ...

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  12. Identify the Quantifiers in the following statements: There exists a ...

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  13. Identify the Quantifiers in the following statements: There exists a ...

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  14. Identify the Quantifiers in the following statements: There exists a...

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  15. Prove by direct method that for any integer n, n^(3)-n is always even.

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  16. Check the validity of the following statement: p:125 is divisible by ...

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  17. Check the validity of the following statement: p:131 is a multiple of...

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  18. Check the validity of the statements given below by the method given a...

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  19. Prove by direct method that for any real numbers x,y if x=y, then x^(2...

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  20. Using contrapositive method prove that if n^(2) is an even integer, th...

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