Verifying that a string contains only letters in C#

I have an input string and I want to verify that it contains:

• Only letters or
• Only letters and numbers or
• Only letters, numbers or underscore

To clarify, I have 3 different cases in the code, each calling for different validation. What's the simplest way to achieve this in C#?

Only letters:

Regex.IsMatch(input, @"^[a-zA-Z]+$");

Only letters and numbers:

Regex.IsMatch(input, @"^[a-zA-Z0-9]+$");

Only letters, numbers and underscore:

Regex.IsMatch(input, @"^[a-zA-Z0-9_]+$");

bool result = input.All(Char.IsLetter);

bool result = input.All(Char.IsLetterOrDigit);

bool result = input.All(c=>Char.IsLetterOrDigit(c) || c=='_');