How to check if a set of key and value already exists in a dictionary

As you've probably discovered, if you Add(key, value) to a Dictionary that already has an entry with the same key, it throws an ArgumentException. It is not possible to have multiple entries with the same key.
If you want to add the value if the key is not present then try this:

Dictionary<int, string> dict = new Dictionary<int, string>();
// initial value for demonstration
dict.Add(1, "umpteen");
dict.Add(2, "di");
// later
if (!dict.Contains(1))
  dict.Add(1, "mono");
// nothing changed in dict
if (!dict.Contains(3))
  dict.Add(3, "three");
// A new key-value pair was added

If all you want it to ensure that a key-value pair exists in the Dictionary, no matter if there is already a key-value pair with the same key and either the same or a different value, then instead of Adding to the Dictionary, just assign into it:

// assume dict as we left it above...
dict[1] = "mono";
dict[2] = "di";
dict[3] = "tri";
dict[4] = "quad";

None of those assignments threw an exception and all 4 entries in the dict are set.

You can use below method to check whether a key is exist or not

ContainsKey(TKey)

And this to check a value

ContainsValue(TValue)