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here are my two tables of concern:

CREATE TABLE IF NOT EXISTS `tutorial` (
  `beggingTime` time NOT NULL,
  `day` varchar(8) NOT NULL,
  `tutorId` int(3) NOT NULL,
  `maxMembers` int(2) NOT NULL,
  `minMembers` int(1) NOT NULL,
  PRIMARY KEY (`beggingTime`,`day`,`tutorId`),
  KEY `tutorId` (`tutorId`)
) 


CREATE TABLE IF NOT EXISTS `group` (
  `groupId` tinyint(3) NOT NULL AUTO_INCREMENT,
  `status` varchar(20) NOT NULL,
  `groupName` varchar(50) NOT NULL,
  PRIMARY KEY (`groupId`)
) 

I would like to create a field in 'group' that would link to the composite unique keys in 'tutorial'. So I guess my question is, how do I relate these tables? do I have to to create foreign keys field in 'group' for each primary key in 'tutorial'?

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Per the mySQL documentation you should be able to set up a foreign key mapping to composites, which will require you to create the multiple columns.

Add the columns and put this in your group table

FOREIGN KEY (`beggingTime`,`day`,`tutorId`) 
    REFERENCES tutorial(`beggingTime`,`day`,`tutorId`)

As Steven has alluded to in the below comments, you SHOULD try to re-architect this so that the tutorial table uses an actual primary key (even if it is just an identity surrogate key). This will allow for greater performance as SQL was built for this type of relationship, not composite.


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