Q14 of 69 Page 261

Prove the following statement by contradication method.

p : The sum of an irrational number and a rational number is irrational.

Let p is false, as the sum of an irrational number and a rational number is irrational.

Let is irrational and n is rational number




But, we know that is irrational where as (r-n) is rational which is contradiction.


Here, Our Assumption is False


Hence, P is true.


More from this chapter

All 69 →
13

Check the validity of the following statement.

p : 125 is divisible by 5 and 7.

 13

Check the validity of the following statement.

q : 131 is a multiple of 3 or 11.

 15

Prove by direct method that for any real numbers x, y if x = y, then x2 = y2.

 16

Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.