requierd problems for select triggered by javascript

Suppose there are two rows of select for id cat and cow, required error message
js omit most

                    <select name="cat1" id="cat1" required>
                        <option value="">ー</option>
                        <option value="1">1</option>
                        <option value="2">2</option>
                        <option value="3">3</option>
                      </select>
                    <select name="cat2" id="cat2" required>
                        <option value="">ー</option>
                        <option value="1">1</option>
                        <option value="2">2</option>
                        <option value="3">3</option>
                      </select>
                    <select name="cow1" id="cow1" required>
                        <option value="">ー</option>
                        <option value="1">1</option>
                        <option value="2">2</option>
                        <option value="3">3</option>
                      </select>
                      <select name="cow2" id="cow2" required>
                        <option value="">ー</option>
                        <option value="1">1</option>
                        <option value="2">2</option>
                        <option value="3">3</option>
                      </select>
                     <div class="errorMsg"></div>
                      <span>一个触发页面跳转页面</span>

<script>
        cat1: function(){
            this.validObj.challenge('cat1', 'cat1') && this.validObj.required();
        },
        cat2: function(){
            this.validObj.challenge('cat2', 'cat2') && this.validObj.required();
        },
        cow1: function(){
            this.validObj.challenge('cow1', 'cow1') && this.validObj.required();
        },
        cow1: function(){
            this.validObj.challenge('cow1', 'cow1') && this.validObj.required();
        },
$.fn.form_check = function(e) {
            var e = e || window.event;
        var page = $.mobile.activePage;
        $('div.inner,input', page).removeClass('error');
        $('p.errorMessage,div.errorBox', page).remove();
        $('span', page).removeClass('admission').removeClass('invalid');
        if (e && $(e.target).closest('a').hasClass('back')) {
            return true;
        }
        var v = new Validator();
        var valid1 = new validationObj({
            validObj: v
        });
        valid1.cat1();
        valid1.cat2();
        valid1.cow1();
        valid1.cow2();
        return !v.has_errors();
    };

In this case, no input error information will be displayed when the four select are not input. Can we disable validiton of cow when the select of the first line of cat1 and cat2 is selected as non-empty option? That is to say, even if the cow select of the second line selects the option of value space-time, it can jump, thank you