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

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You watch television if and only if your mind is free.
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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.

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

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Rewrite each of the following statements in the form 'p if and only if q'. Give below are pairs of statements. Combine them using 'if and only if' : p : If two lines are parallel, then their slopes are equal. q : If the slopes of two lines are equal, then they are parallel.

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RD SHARMA-MATHEMATICAL REASONING-Solved Examples And Exercises
  1. State the converse and contrapositive of the following statement: If...

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  2. State the converse and contrapositive of the following statement: If...

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  3. Rewrite the following statements in the form p if only ifq : if yo...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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