This is the
counter example Thus, we have proved that the generalisation “For each n,
22
1
n +  is a prime
(n ∈ N)” is not true in general Rationalised 2023-24
PROOFS IN MATHEMATICS
195
Example 9 Every continuous function is differentiable Proof  We consider some functions given by
(i)
f (x) = x2
(ii)
g(x) = ex
(iii)
h(x) = sin x
These functions are continuous for all values of x