You should create 2 select question on same page, first as single select ans second as multi-select.

Do you want to choose either from single select or mutli-select, if yes, you also need to make both as optional and use javascript for validation. If this is not requirement, you don't do anything.

Here is the code to use in footer to select and de-select radio button and checkbox
[js]
<script type=\"text/javascript\">
function SSI_CustomGraphicalCheckbox(GraphicalCheckboxObj, InputObj, blnCheck)
{
\tif(InputObj.name == \"Q1b_1\" && blnCheck == true)
\t{
\t\tSSI_RadioReset(\"Q1a\");
\t}
\tif(InputObj.name == \"Q1b_2\" && blnCheck == true)
\t{
\t\tSSI_RadioReset(\"Q1a\");
\t}
\tif(InputObj.name == \"Q1b_3\" && blnCheck == true)
\t{
\t\tSSI_RadioReset(\"Q1a\");
\t}
\tif(InputObj.name == \"Q1b_4\" && blnCheck == true)
\t{
\t\tSSI_RadioReset(\"Q1a\");
\t}
\tif(InputObj.name == \"Q1b_5\" && blnCheck == true)
\t{
\t\tSSI_RadioReset(\"Q1a\");
\t}
}
function SSI_CustomGraphicalRadiobox(GraphicalRadioboxObj, InputObj)
{
\tif(InputObj.name == \"Q1a\")
\t{
\t\tSSI_SetSelect(\"Q1b_1\", false);
\t\tSSI_SetSelect(\"Q1b_2\", false);
\t\tSSI_SetSelect(\"Q1b_3\", false);
\t\tSSI_SetSelect(\"Q1b_4\", false);
\t\tSSI_SetSelect(\"Q1b_5\", false);
\t}
}
</script>
[/js]

Combining radio buttons and check box in a select-type question