The burden of proof lays in the hands of the person that doubts it to be true. They must find evidence to the contrary of your statement. If this is not the case then everything must be false as with the pre-mentioned Monday/Tuesday example
With your logic I can say that you re Muslim gay rapist that eats kids alive and it is true until you disprove it...
Weekdays are artificial constructs to "divide time" they are no real-world elements thus there is no need for evidence. Weekdays does not really exist. Lets say that you have just waked up from long coma, there is no way how to say which weekday is until you look in calendar, because weekdays are functions of calendar, not functions of real world.