If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

The Cartesian product R × R represents the set R × R={(x, y) : x, y Î R} which represents the coordinates of all the points in two dimensional space and...

Solution: (i) 43.123456789  Since this number has a terminating decimal expansion, it is a rational number of the form / and q is of the form 2×5 i.e., the prime factors of q...

Solution: The product of a rational number and an irrational number can be a rational number or an irrational number. Examples: i. rational number = 0 irrational number = √2 => 0 x √2 = 0, which...

The product of a non zero rational and an irrational number is always irrational 

Solution: i. Since the given number has a terminating decimal expansion, it is a rational number of the form p/q and q is of the form 2m x 5n. The prime factors of...

(i) 0 (ii) 1 and -1 (iii) 0

Thanks a lot for this answer !! I had solved it already but there were some minor mistakes in my answer. This helped me to correct it. Thanks !!!

R: set of real numbers Q: set of rational numbers Therefore, R – Q is a set of irrational numbers.

(b) :  f (x) is discontinuous at every x, except x = 0