JSFiddle - React, Tailwind, and code Playground

HTML

<select id="first">
    <option value="none">None</option>
    <option value="one">Toyota</option>
    <option value="two">Nissan</option>
</select>

<select id="second">
    <option value="none">None</option>
    <option value="one">Toyota</option>
    <option value="two">Nissan</option>
</select>

JavaScript

$("#first").change(function() {
    switch($("#first").val()) {
        case "one":
            $("#second option[value='one']").hide();
            $("#second option[value!='one']").show();
            $("#second").val("none");
            break;
        case "two":
            $("#second option[value='two']").hide();
            $("#second option[value!='two']").show();
            $("#second").val("none");
            break;
        case "none":
            $("#second option[value='one']").show();
            $("#second option[value!='two']").show();
            $("#second").val("none");
            break;
    }
});

$("#second").change(function() {
    switch($("#second").val()) {
        case "one":
            $("#first option[value='one']").hide();
            $("#first option[value!='one']").show();
            $("#first").val("none");
            break;
        case "two":
            $("#first option[value='two']").hide();
            $("#first option[value!='two']").show();
            $("#first").val("none");
            break;
        case "none":
            $("#first option[value='one']").show();
            $("#first option[value!='two']").show();
            $("#first").val("none");
            break;
    }
});