<p class="first">
    <p class="first-child"></p>
</p>
<p class="second">
    <p class="second-child">
        <p class="second-child-child"></p>
    </p>
</p>
<script type="text/javascript">
    var a = document.querySelector('.first-child');
    var b = document.querySelector('.second-child-child');
    var c = document.querySelector('.first');
    var d = document.querySelector('.second');

    function isChildOf(child, parent) {
        var parentNode;
        if(child && parent) {
            parentNode = child.parentNode;
            while(parentNode) {
                if(parent === parentNode) {
                    return true;
                }
                parentNode = parentNode.parentNode;
            }
        }
        return false;
    }

    console.log(isChildOf(a, b));
    console.log(isChildOf(b, d));
    console.log(isChildOf(a, c));
</script>

<p class="parent">

<p class="child"></p>

</p>
console.log(document.querySelector(".parent").querySelector(".child"))
child存在时有值,不存在值是null,判断这个就行了