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Rewrite the following statement in the form `p` if only if`q :` `r :` For you to get an A grade, it is necessary and sufficient that you do all the homework you regularly.

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You get an A grade if and only if you do all the homework regularly.
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Rewrite each of the following statements in the form “p if and only if q" (i) p: If you watch television, then your mind is free and if your mind is free, then you watch television. (ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly. (iii) r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Write each of the following using 'if and only if': (i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly. (ii) If you watch television then your mind is free and if your mind is free then you watch television.

Write each of the following statements in the form 'if p, then q' : To pass in examination it is necessary that you work hard.

Write each of the following statements in the form 'if p, then q' : You earn a living implies you work.

Rewrite each of the following statements in the form p if only if q:p: if you watch television then your mind is free and if your mind is free,then you watch television.

Rewrite the following statements in the form: 'p if and only if q' p: A quadrilateral is equiangular. q: A quadrilateral is a rectangle.

Of the following statements, which one do you agree with?

Rewrite each of the following statements in the form p if only if q:q: Lf a quadrilateral is equiangular,then it is a rectangle and if a quadrilateral is a you rectangle,then it is equiangular.

RD SHARMA-MATHEMATICAL REASONING-Solved Examples And Exercises
  1. Rewrite the following statements in the form p if only ifq : if yo...

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  2. Rewrite the following statement in the form p if only ifq : q : if ...

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  3. Rewrite the following statement in the form p if only ifq : r : For...

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  4. Rewrite the following statement in the form p if only ifq : If a tum...

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  5. Determine the contrapositive of each of the following statements: (i)I...

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  6. Determine the contrapositive of each of the following statements: (i)I...

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  7. Determine the contrapositive of each of the following statements: (i)O...

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  8. Determine the contrapositive of each of the following statements: (i)I...

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  9. Given below are two statements: p : 80 is a multiple of q : 80 is a m...

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  10. If p\ a n d\ q are two statement given by: p : 25 is multiple of 5. q ...

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  11. Given below are two statement: p : 25 is a multiple of 5. q : 25 is a ...

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  12. Check the validity of the following statement: “Square of an integer i...

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  13. Check whether the following statement is true or not: If x\ a n d\ y a...

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  14. Check whether the following statement is true and false by proving its...

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  15. Show that the statement: p : If\ x is a real number such that x^3+4x=0...

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  16. Show that he following statement is true by the method of contrapos...

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  17. Using the words necessary and sufficient rewrite the statement The int...

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  18. Verify by the method of contradiction that sqrt(7) is irrational.

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  19. Check the validity of the statement given below by contradiction metho...

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  20. Evaluate the following limit: (lim)(x->0)(x^2+1-cos x)/(xsinx)

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