Miscellaneous Exercise

Check the validity of the statements given below by the method given against it. (i) p: The sum of an irrational number and a rational number is irrational (by contradiction method). (ii) q: If n is a real number with n > 3, then n2 > 9 (by contradiction method).

(I) The given assertion is as per the following p: The amount of a silly number and a judicious number is silly. Allow us to expect that the assertion \[p\] is bogus. That is, The amount of a...

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Given below are two statements p: 25 is a multiple of 5. q: 25 is a multiple of 8. Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.

The compound assertion with \['And'\] is as per the following \[25\]is a various of \[5\text{ }and\text{ }8\] This is bogus articulation since \[25\] is definitely not a numerous of \[8\] The...

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Re write 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.

(I) You stare at the TV if and provided that your brain is free (ii) You get A grade if and provided that you do all the schoolwork consistently

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