Answer:
Contradictory Statement
Step-by-step explanation:
In contradictory statement , we basically describes a proof by assuming opposite of what we want to prove .
For example :
Prove that [tex]\sqrt{2}[/tex] is irrational .
Solution :
We will prove this by contradiction .
Let if possible [tex]\sqrt{2}[/tex] is rational .
[tex]\sqrt{2}=\frac{p}{q}[/tex] where p and q are integers and coprime such that [tex]q\neq 0[/tex]
On squaring both sides , we get
[tex]2q^2=p^2\\\Rightarrow 2|p^2\\\Rightarrow 2|p[/tex]
we get ,
p=2r
On squaring both sides, we get
[tex]p^2=4r^2\\\Rightarrow 2q^2=4r^2\\\Rightarrow q^2=2r^2\\\Rightarrow 2|q^2\\\Rightarrow 2|q[/tex]
So, 2 divides p and q which is a contradiction to the fact that p and are coprime .
Therefore, [tex]\sqrt{2}[/tex] is irrational .
