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...

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

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

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

 (a) According to the question,  x + x + 2 + x + 4 + x + 6 + x + 8 = 140  or, 5x + 20 = 140  or, 5x =...