Madhya Pradesh Board Solutions for Chapter: Proofs in Mathematics Appendix 1, Exercise 4: EXERCISE

Find counter-example to disprove the following statement

A quadrilateral with all angles equal is a square.

Find counter-example to disprove the following statement : 

For integers $a$ and $b$, $\sqrt{a^2+b^2}=a+b$

Find counter-example to disprove the following statement :

$2n^2+11$ is a prime for all whole numbers $n$.

Find counter-examples to disprove the following statement :

$n^2-n+41$ is a prime for all positive integers $n$.

Prove that the sum of two odd numbers is even.

Prove that the product of two odd numbers is odd.

Prove that the sum of three consecutive even numbers is divisible by $6$.

Prove that infinitely many points lie on the line whose equation is $y=2x$

(Hint : Consider the point $\left(n, 2n\right)$ for any integer $n$)