Question

Rewrite the following statements formally using the quantifiers for all or for every and theres as appropraite . a)Not all continous functions are differentiable b) for real x,2x is never negative.

Answer 1

There exist a continuous function which is not differentiable,

`2^x\geq 0` For all real number x.

Explanation:

Consider the provided information.

We need to Rewrite the following statements formally using the quantifiers

The two quantifiers are: 'there exists' and 'for all.'

Now use them in order to change the statements.

Part (a) Not all continuous functions are differentiable

The quantifier statement is:

There exist a continuous function which is not differentiable,

Part (b) for real x,2x is never negative.

The quantifier statement is:

`2^x\geq 0` For all real number x.