Edit in JSFiddle

var MyApp = angular.module('MyApp', []);

MyApp.service('Set', function(){
  return {
    intoSet: function(arr){
      var set = [];

      arr.forEach(function(item){
        if(set.indexOf(item) < 0){
          set.push(item);
        } 
      });

      return set;
    },

    union: function(arrA, arrB){
      var setA = this.intoSet(arrA);
      var setB = this.intoSet(arrB);
        
      setB.forEach(function(item){
        if(setA.indexOf(item) < 0){
          setA.push(item);
        } 
      });

      return setA;
    },

    intersection: function(arrA, arrB){
      var setA = this.intoSet(arrA);
      var setB = this.intoSet(arrB);

      var intersected = [];

      setA.forEach(function(item){
        if(setB.indexOf(item) >= 0){
          intersected.push(item);
        } 
      });

      return intersected;
    }
  }
});

MyApp.controller('MyController', function($scope, Set) {    
    $scope.union = function(){
       var arrA = $scope.arrA.split(',');
       var arrB = $scope.arrB.split(',');
       
       $scope.result = Set.union(arrA, arrB).toString();
    }
    
    $scope.intersection = function(){
       var arrA = $scope.arrA.split(',');
       var arrB = $scope.arrB.split(',');
       
       $scope.result = Set.intersection(arrA, arrB).toString();
    }
});

<div ng-controller="MyController">
   <p>
       <input type="text" placeholder="Ensimmäinen joukko" ng-model="arrA">
   </p>
   <p>
       <input type="text" placeholder="Toinen joukko" ng-model="arrB">
   </p>
   <p>
       <button ng-click="union()">Unioni</button>
       <button ng-click="intersection()">Leikkaus</button>
   </p>
   <p>
       Lopputulos: {{result}}
   </p>
</div>