Plugin settings not saving

the problem is you keep resting the values here:

 $options = array(
        'cemb_seminar_seminars_college' => '0',
        'cemb_seminar_showcases_college' => '0',
        'cemb_seminar_writers_college' > '0',
        'cemb_seminar_aet_college' => '0',
        'cemb_seminar_mbu_college' => '0',
        'cemb_seminar_eis_college' => '0',
        'cemb_seminar_sng_college' => '0',
    );
    update_option( 'cemb_seminar_options', $options );

change it to

$options = get_option('cemb_seminar_options');
if ($options === false){
$options = array(
            'cemb_seminar_seminars_college' => '0',
            'cemb_seminar_showcases_college' => '0',
            'cemb_seminar_writers_college' > '0',
            'cemb_seminar_aet_college' => '0',
            'cemb_seminar_mbu_college' => '0',
            'cemb_seminar_eis_college' => '0',
            'cemb_seminar_sng_college' => '0',
        );
        update_option( 'cemb_seminar_options', $options );
}

so it will only run if ‘cemb_seminar_options’ is not set in the database