InterviewSolution
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InterviewSolution
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check the validity of the following statement (a) r : if x is a real number such that x^3+9x then x is 0. (b) r : If x is an integer and x^3 is even , then x is also even (c) r : If a polygon regular thon it is equiangular and equilateral. |
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Answer» Solution :(a) Component STATEMENTS are p : X is a real number such that `x^3+9x=0` Q : x is 0 Now to check validity of r (i) Direct Method : Let p is true, then q is true. `therefore` x is real number such that `x^3+9x=0` `therefore` x is a real number such that `x(x^2+9)=0` `therefore x=0` `therefore` q is true Thus , p is true `rArr` q is true So, given statement r is true (ii) Contrapositive Method : Let q is false , i.e.,`x ne 0` Now , according to p x is real number such that `x^3+9x=0` So, `x(x^2+9)=0` It shows that x is real number and x=0 , but according to q , `x ne 0` , so this is a contradiction So, r is true Component statement are p : x is an integer and `x^3` is even q : x is an even integer Suppose q is false (i.e.,~q is true) i.e.,x is an odd integer So, `x^3= " odd"xx "odd"xx"odd "` `=" (odd"xx "odd)"xx"odd "` `" odd"xx "odd"` `x^3` is also odd , so p is false It shows that `~q rArr ~p` (C) Component statements of r be p : A polygon is REGULAR. q : A polygon is equiangular and equilateral. |
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