In SQL does a Primary Key in a create table enforce uniqueness?

Question

Im wondering if on a relational table I set the two values below as a PRIMARY KEY if that automatically makes the table know that all entries should be unique....

CREATE TABLE UserHasSecurity
(
    userID int REFERENCES Users(userID) NOT NULL,
    securityID int REFERENCES Security(securityID) NOT NULL,
     PRIMARY KEY(userID,securityID)
)

or do I need to be more explicit like this...

CREATE TABLE UserHasSecurity
(
    userID int REFERENCES Users(userID) NOT NULL,
    securityID int REFERENCES Security(securityID) NOT NULL,
     PRIMARY KEY(userID,securityID),
     UNIQUE(userID,securityID)
)

Answer 1

You don't need UNIQUE here. PRIMARY KEY will make sure there is no duplicate (userID,securityID) pairs.

Answer 2

No, you don't need to specify UNIQUE in addition to PRIMARY KEY. A primary key by definition must be unique.

Answer 3

A PRIMARY KEY has to be unique, so you only need to declare as a primary key. The underlying index is unique by definition.

Creating Unique Indexes