Laravel issue with related models

I have three tables: User, Product and Purchase

User: id, email
Product: id, name
Purchase: user_id, product_id, transaction_id

In Laravel, I have defined these models:

class User extends Authenticatable { 
    //only protected $$fillable and $hidden fields
}

class Product extends Model {
    //only protected $$fillable and $hidden fields
}

class Purchase extends Model {
    public function user() {
        return $this->hasOne('App\Models\Access\User\User');
    }

    public function product() {
        return $this->hasOne('App\Models\Modules\Product');
    }
}

The idea is that I can find out which user has purchased which products so that (in my view) I can loop over the products and indicate which ones have been purchased already by that user

I can put an extra column 'purchased' into products (which I can fill once the purchase was successfull) but I would rather avoid this because I feel I have all the information available.

Anyone has a suggestion how I could achieve this?

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