SOURCE

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

<div id="app">
  <p :class="{ red: red_isActive, big: big_isActive }">23333</p>
  <button @click="isClassActive()">active or not</button>
</div>

.red{
  background-color: red;
}

.big{
  font-size: 3em;
}