[Vuejs]-Dependent dropdown with vue js (without ajax)

You missunderstood computed. Also, I would advise to use === , not ==

Your computed should be show :

computed: {
    show (): {
      if (this.value === this.val1) {
        return true;
      }
     else
        return false;
    }
}

Try to create quick JSFiddle if the issue is still there and I will help you to fix it.