Question

(a) Write the negation of the statement,

“√2 is not a complex number”

(b) Write the converse and contrapositive of the statement,

“If a triangle is equilateral, then it is isosceles”

(c) Verify by the method of contradiction that “√3 is irrational”​

Answer 1

Step-by-step explanation:

(a) √2 is a rational number.

(b) If a Triangle is Isosceles It cant be equilateral.

(c) Let √3 be a rational

Therefore, √3=a/b

Therefore, √3b=a

Squaring Both Sides, (√3b)^2=a^2

we get 3b^2=a^2

Now Taking Value Of a Such that it is similar to √3

Therefore, a=3c

3b^2=(3c)^2

So 3b^2=9c^2

Now b^2/=9c^2/3

Therefore, b^2=3c^2

Therefore,

b^2

----- =3

c^2

Hence, Proved That √3 is An Irrationality Number.