Which of the following conditions imply that the real number x is rational ?
`(i) x^(1//2)"is rational"" "(ii) x^(2)and x^(5) "are rational"" "(iii) x^(2)and x^(4)"are rational"`

Which of the following conditions necessarily imply that the real number x is rational,I x^(2) is rational II x^(3) and x^(5) are rational III x^(2) and x^(3) are rational

Which of the following conditions necessarily imply that the real number x is rational, I x^2 is rational II x^3 and x^5 are rational III x^2 and x^3 are rational

Which of the following conditions necessarily imply that the real number x is rational, I x^2 is rational II x^3 and x^5 are rational III x^2 and x^3 are rational

(x+y)/(2) is a rational number.

Let f(x)=[x^(2) if x is irrational,1 if x is rational then

Which one of the following is false : (i) Every rational number is a real number (ii) Every integer is a real number (iii) sqrt2 is a rational number

Which of the following are empty (null) sets ? (i) [x:xlt5andxgt7,x inN} (ii) {x:x^(2)=25and x is an odd integer} (iii) {x:x^(2)-2=0 and is rational ]

Are the following pairs of statements negations of each other: The number x is not a rational number. The number x is a rational number.

Are the following pairs of statements negations of each other: (i) The number x is not a rational number. The number x is not an irrational number. (ii) The number x is a rational number. The number x is an irrational number.