const app = Vue.createApp({
  data() {
    return {
      isVisible: true
    }
  },
  methods: {
    toggle() {
      this.isVisible = !this.isVisible
    }
  }
})

app.mount('#app')

<!-- template -->
<div id="app">
  <button @click="toggle">Toggle message</button>
  <p v-show="isVisible">This paragraph stays in the DOM.</p>
</div>