Save Multiple Grouped checkbox array to database

Hi. Im completely baffled on how to save multiple groups of arrays to a database or even if its possible.

What im trying to do is

@foreach($customers as $customer)
<input type="checkbox" name="activity_1[]" value="1">
    Pre-Book this for <strong>{{ $customer->name }}</strong>
@endforeach 


@foreach($customers as $customer)
<input type="checkbox" name="activity_2[]" value="1">
    Pre-Book this for <strong>{{ $customer->name }}</strong>
@endforeach 

@foreach($customers as $customer)
<input type="checkbox" name="activity_3[]" value="1">
    Pre-Book this for <strong>{{ $customer->name }}</strong>
@endforeach 

So there could be 1-3 customers in each activity.

I want to do it so it saves to the database as a relationship

So the database is like this::

customer 1

• id = 1
• customer_id = 1
• activity_1 = true
• activity_2 = false
• activity_3 = true

customer 2

• id = 2
• customer_id = 2
• activity_1 = true
• activity_2 = true
• activity_3 = true

Any help would be greatful. I have tried this::

$activities = $request->activity_1;
$activities_2 = $request->activity_2;
$activities_3 = $request->activity_3;

foreach ($activities as $index => $activity) {
    $activity = new Activity();
    $activity->activity_1 = $activity;
    $activity->activity_2 = $activity_2[$index];
    $activity->activity_3 = $activity_3[$index];
    $activity->save();
}

but i get 0 in the columns. but if i return the $activities array it shows that its ok.