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Write down the negation of the following compound statements:
(i) All rational numbers are real and complex.
(ii) All real number are rational or irrational.
(iii) $\mathrm{x}=2$ and $\mathrm{x}=3$ are roots of the quadratic equation $x^2-5 x+6=0$
(iv) A triangle has either 3-sides or 4-sides.
(v) 35 is a prime number or a composite number.
(vi) All prime integers are either even or odd.
(vii) $|x|$ is equal to either $x$ or $-x$.
(viii) 6 is divisible by 2 and 3 .
(i) All rational numbers are real and complex.
(ii) All real number are rational or irrational.
(iii) $\mathrm{x}=2$ and $\mathrm{x}=3$ are roots of the quadratic equation $x^2-5 x+6=0$
(iv) A triangle has either 3-sides or 4-sides.
(v) 35 is a prime number or a composite number.
(vi) All prime integers are either even or odd.
(vii) $|x|$ is equal to either $x$ or $-x$.
(viii) 6 is divisible by 2 and 3 .
Solution:
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Verified Answer
(i) It is false that all rational numbers are real and complex.
(ii) It is false that all real numbers are rational or irrational.
(iii) $\mathrm{x}=2$ is not a root of the quadratic equation $\mathrm{x}^2-5 \mathrm{x}+$ $6=0$ or $x=3$ is not a root of the quadratic equation $x^2-5 x+6=0$.
(iv) A triangle has neither 3 -sides nor 4-sides
(v) 35 is not a prime number and it is not a composite number.
(vi) It is false that all prime integers are either even or odd.
(vii) $|x|$ is not equal to $x$ and it is not equal to $-I$.
(viii) 6 is not divisible by 2 or it is not divisible by 3 .
(ii) It is false that all real numbers are rational or irrational.
(iii) $\mathrm{x}=2$ is not a root of the quadratic equation $\mathrm{x}^2-5 \mathrm{x}+$ $6=0$ or $x=3$ is not a root of the quadratic equation $x^2-5 x+6=0$.
(iv) A triangle has neither 3 -sides nor 4-sides
(v) 35 is not a prime number and it is not a composite number.
(vi) It is false that all prime integers are either even or odd.
(vii) $|x|$ is not equal to $x$ and it is not equal to $-I$.
(viii) 6 is not divisible by 2 or it is not divisible by 3 .
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