SOURCE

let app = new Vue({
	el: '#app',
  data: {
    app_class: {
      red: true,
      big:true
    },
  },
  methods: {
    isClassActive: function () {
      this.app_class.red = !this.app_class.red;
      this.app_class.big = !this.app_class.big;
    }
  }
});

<div id="app">
  <p :class="app_class">23333</p>
  <button @click="isClassActive()">active or not</button>
</div>

.red{
  background-color: red;
}

.big{
  font-size: 3em;
}