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Using the words necessary and sufficient...

Using the words necessary and sufficient rewrite the statement The integer n is odd if and only if `n^2`is odd. Also check whether the statement is true.

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The necessary and sufficient condition that the integer n be odd is `n^2` must be odd
Let p and q denote the statement
p:the integer n is odd
q:`n^2` is odd
...
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NCERT-MATHEMATICAL REASONING-SOLVED EXAMPLES
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  2. Write the contra positive of the following statement:(i)         If a ...

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  3. Write the negation of the following statements.(i) Both the diagonals...

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  4. Write the negation of the following statements and check whether the ...

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  5. Check whether the following sentences are statements. Give reasons fo...

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  6. Write the component statements of the following compound statements a...

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  7. For each of the following statements, determine whether an inclusive ...

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  8. Find the component statements of the following compound statements. (...

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  9. 5 Find the component statements of the following and check whether the...

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  10. Verify by the method of contradiction. p:sqrt(7)is irrational.

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  11. Check whether the following statement is true of false by proving its...

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  12. Cheek whether Or used in the following compound statement is exclusiv...

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  13. By giving a counter example, show that the following statement is fal...

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  14. For each of the following compound statements, first identify the cor...

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  15. Write the converse of the following statements.(i) If a number n is e...

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  16. Check whether the following statement is true or not. If x, y in Zar...

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  17. Given below are two pairs of statements. Combine these two statements...

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  18. For the given statements identify the necessary and sufficient condit...

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  19. Using the words necessary and sufficient rewrite the statement The in...

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  20. Write the negation of the following statements:(i) p: For every real ...

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