If a is rational and b is irrational, show that :
a - b

If (log)_a x=b for permissible values of a and x , then identify the statement(s) which can be correct. (a)If a and b are two irrational numbers, then x can be rational. (b)If a is rational and b is irrational, then x can be rational. (c)If a is irrational and b is rational, then x can be rational. (d)if aa n d b are rational, then x can be rational.

Prove the following by contradiciton ."The sum of a rational and an irrational number is an irrational number?".

Find the value of x where f(x)={x ,if x is rational 1-x ,if x is irrational is continuous dot

If f(x)={x ,x is rational 1-x ,x is irrational ,then f(f(x)) is

Two mappings f:R to R and g:R to R are defined as follows: f(x)={(0,"when x is rational"),(1,"when x is irrational"):} and g(x)={(-1,"wnen x is rational"),(0,"when x is irrational"):} then the value of [(gof)(e)+(fog)(pi)] is -

Show that the sum of a rational number and an irrational number cannot be rational.

Prove the following by contradiction : "The sum of a rational and irrational number is an irrational number ."

If f(x) = 2x + 3, then x is rational. =x^(2)+1 , when x is irrational. then find - (a) f(0), (b) f(pi) .

Define an irrational number and show that sqrt(5) is an irrational number.