Number of irrational numbers are greater than the number of rational numbers.
State, in each case, whether the given statement is true or false.
(i) The sum of two rational numbers is rational.
(ii) The sum of two irrational numbers is irrational.
(iii) The product of two rational numbers is rational.
(iv) The product of two irrational numbers is irrational.
(v) The sum of a rational number and an irrational number is irrational.
(vi) The product of a nonzero rational number and an irrational number is a rational number.
(vii) Every real number is rational.
(viii) Every real number is either rational or irrational.
(ix) π is irrational and 227 is rational.
Are there more rational numbers than irrational numbers?
Are rational and irrational numbers real numbers?
Are the followingpairs of statements negations of each other?
(i) The number xisnot a rational number.
The number xis not an irrational number.
(ii) The numberx isa rational number.
The number xis an irrational number.