f is defined in [–5, 5] as f(x) = { (x, if x is rational and), (-x, if x is rational).

R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}  ∴ R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}  ∴ Domain of...

R = {(a, b): a, b ∈ Z, a – b is an integer} It is known that the difference between any two integers is always an integer.  ∴ Domain of...

A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n  Prime factor of 9 = 3  Prime factors of 10...

R = {(a, b): a, b ∈ N and a = b2}  (i) It can be seen that 2 ∈ N; however, 2 ≠ 22 = 4.  Therefore, the statement “(a, a)...

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 

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

yes zero is a rational number. it can be written as 0/1,0/2 etc, in the form p/q where p and q are integers and q ≠0 ? 

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

A +B=? How?