<style>
  .red {
    color:red;
    /*color:#ff8800;*/
  }
  .bg {
    background: #000;
    /*background: green;*/
  }
  </style>


  window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
        red_color : 'red',
        bg_color : 'bg'
      }
    });
  }



  <div id="box">
    <span :class="[red_color,bg_color]">this is a test string</span>
  </div>

<style>
  .red {
    color:red;
  }
  .bg {
    background: #000;
  }
  </style>

  window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
      }
    });
  }
  
  <div id="box">
    <span :class="{red:true,bg:true}">this is a test     string</span>
  </div>

<style>
  .red {
    color:red;
  }
  .bg {
    background: #000;
  }
  </style>

  window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
        r : true,
        b : false
      }
    });
  }

  <div id="box">
    <span :class="{red:r,bg:b}">this is a test string</span>
  </div>

<style>
  .red {
    color:red;
  }
  .bg {
    background: #000;
  }
  </style>

  window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
        json : {
          red : true,
          bg : false
        }
      }
    });
  }


  <div id="box">
    <span :class="json">this is a test string</span>
  </div>

window.onload = function(){
    var c = new Vue({
      el : '#box',
    });
  }

   <div id="box">
    <span :style="{color:'red',background:'#000'}">this is a test string</span>
  </div>

window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
        c : {
          color : 'green'
        }
      }
    });
  }

  <div id="box">
    <span :style="[c]">this is a test string</span>
  </div>

window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
        c : {
          color : 'green'
        },
        b : {
          background : '#ff8800'
        }
      }
    });
  }

<div id="box">
     <span :style="[c,b]">this is a test string</span>
  </div>

window.onload = function(){
    var c = new Vue({
      el : '#box',
      data : {
        a : {
          color:'yellow',
          background : '#000'
        }
      }
    });
  }

<div id="box">
     <span :style="a">this is a test string</span>
</div>