[Solved]-Contains<T>() and how to implement it-LINQ,C#

You could create the extension method

public static bool Contains(this IList<Person> list, string name) {
    return list.Any(c => c.Name == name);
}

The solutions already presented by Jon Skeet and yapiskan are the way to go. If you need exactly what you're stating then you could write an extension method:

public static class ContactListExtensions
{
    public static bool Contains<T>(this List<Person> contacts, string aPersonName)
    {
        //Then use any of the already suggested solutions like:
        return contacts.Contains(c => c.Name == aPersonName);
    }
}  

I'd agree with Jon's Any, but if you are stuck with C# 2.0, or C# 3.0 with .NET 2.0/3.0 and no LINQBridge, then another approach is List<T>.Find or List<T>.Exists. I'll illustrate with Find, since Exists got posted just as I was about to hit the button ;-p

// C# 2.0
bool knowsFred = person.Contacts.Find(delegate(Person x) { return x.Name == "Fred"; }) != null;
// C# 3.0
bool knowsFred = person.Contacts.Find(x => x.Name == "Fred") != null;

I'm assuming the Contacts is the Contacts for the person in question (person in your code snippit)

List has a contains method that takes an object of type T as a parameter and returns true or false if that object exists in the list. What your wanting is IList.Exists method, Which takes a predicate.

example (c# 3.0)

bool hasContact = person.Contacts.Exists(p => p.Name == "aPersonName");

or (c# 2.0)

bool hasContact = person.Contacts.Exists(delegate(Person p){ return p.Name == "aPersonName"; });