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You didn’t give the script part so i’m going to do some assumptions..
In any case, you can use $emit that will send a signal to the "father component(the component that passed the menu prop)" and you can receive that signal in the father component using @emitName and changing the value there
Example:
<v-btn @click="$emit('cancel')" color="primary" text>Cancel</v-btn>
In the father component:
<SonComponent :menu="menuData" @cancel="menu=false" />
You can learn more from this here
Hope this helps.
Source:stackexchange.com