Form refreshes after clicking Submit - html

Question

Both of these methods successfully send the data, but refresh the form (I'm trying to keep it hidden via jquery after clicking submit)
#1) <button type="submit" class="btn btn-info" value="Submit" id="submit">SUBMIT</button>
#2) <input type="submit" class="btn btn-info" value="Submit" id="submit">
Based on other solutions, I tried these 2 approaches. While they don't refresh the form, they don't send the data either.
#3) <button type="submit" class="btn btn-info" value="Submit" id="submit" onclick="return false;">SUBMIT</button>
#4) <input type="submit" class="btn btn-info" value="Submit" id="submit">
Entire code:
<?
if (!empty($_POST)) {
include_once 'form.php';
$message = 'Thank You';
}
?>
-----------
<script>
$(document).ready(function() {
$('input[type="radio"]').click(function() {
if($(this).attr('id') == 'other_radio') {
$('#other').show();
} else {
$('#other').hide();
}
});
});
</script>
-----------
<div class ="form-hide">
<form method="post" role="form" id="survey">
<div class="form-group">
<label>How did you hear about us?</label>
<div class="radio">
<label><input type="radio" name="howdidyouhearaboutus" value="Facebook">Facebook</label>
</div>
<div class="radio">
<label><input type="radio" name="howdidyouhearaboutus" value="Online Ad">Online Ad</label>
</div>
<div class="radio">
<label><input type="radio" name="howdidyouhearaboutus" value="TripAdvisor">TripAdvisor</label>
</div>
</div>
<div class="form-group">
<input type="submit" class="btn btn-info" value="Submit" id="submit" onclick="return false;">
</div>
</form>
<? if ($message): ?>
<div class="text-center alert alert-success">
<?= $message ?>
</div>
<? endif; ?>
</div>
--------------------
<script>
$('#submit').click(function(){
$('.form-hide').hide();
});
</script>
And form.php is for Google Sheets API integration, not sure if I need to include that here?
$client = new Google_Client();
try {
$client->setAuthConfig('account.json');
} catch(Exception $ex) {
exit('account.json not found.');
}
$client->setScopes(['https://www.googleapis.com/auth/drive','https: //spreadsheets.google.com/feeds']); ........