I’m sorry if this seems dumb. I tend to take things literally and “mutual” and “exclusive” seem to be antonyms but mutually exclusive is a term used a lot and it confuses the crap out of me. I’m a native English speaker also.
Does it mean that the two things CAN exist together? I feel like my brain does gymnastics trying to understand the term; I’m not a dumb person but this term just totally eludes me!
Please don’t attack me, just trying to not feel stupid.
In: 49
It means two things which cannot co-exist.
Hot snow, wealthy poor people, loud silence etc etc
The term “mutually exclusive” simply means that two things by definition cannot exist or coexist together or at the same time.
For example if you were to flip a coin getting heads is mutually exclusive with getting tails. The coin cannot land on both sides simultaneously.
Usually the phrase refers to attributes which can’t both be simultaneously true. “It’s a green light” and “it’s a red light” are mutually exclusive phrases (at least about the same light). “It’s a windy day” and “it’s a hot day” are not mutually exclusive.
These answers are all great. I think maybe it’s the “mutually” part that is confusing you. It just means that each element, by itself, *means* that the other one cannot be present. If a coin lands heads, that *means* it cannot simultaneously have landed tails. If a man is a bachelor, that *means* he cannot simultaneously be married. Each element of the expression excludes the other – they **both** have that property. They mutually exclude each other.
Mutually exclusive means that a excludes b, and b excludes a. They exclude each other mutually.
If I say you can have a pizza and the toppings can be pepperoni and sausage, sausage and peppers, pepperoni and ham, and ham and peppers, then that means that sausage and ham are mutually exclusive. You can can sausage on the pizza with another topping, but that excludes ham. You can also have ham with another topping, but the ham excludes the sausage.
It means that one thing existing excludes the existence of the other thing. Because this goes both ways, it’s mutual. Once one of it exists, the other cannot.
“Mutually exclusive” means that picking A would exclude B, *and also* picking B would exclude A.
There are two cookies. You can pick one and I’ll take the other. If you take the chocolate chip cookie, then you have excluded the cinnamon cookie because I’m going to take it. But also, if you take the cinnamon cookie then you have excluded the chocolate chip…because I’m going to take it. There is no option where you get both, because no matter what you pick, you exclude something – the choices are mutually exclusive.
A choice between “eat the cookie” or “save it for later” is not *mutually* exclusive because picking “eat the cookie” excludes any option to save it for later…but picking “save it for later” does *not* exclude the possibility of “eat the cookie” because you can still eat it later.
First, let me say that the other answers here are great. They give you a good idea of what the words are trying to say.
I kinda get what you mean, though. The implication of *mutually* exclusive is that you could somehow have a situation where **A** implies ***not* B**, but that **B** would still somehow allow **A**.
This doesn’t work, because if you have **B**, there is no way you can have **A**, as that would introduce a contradiction. Imagine that you have **B** and **A**…well, the first rule says that if you have **A**, you cannot have **B**: and there is our contradiction.
It can make your head swim a bit.
I agree with you that it’s a bit of an unfortunate phrase. Ultimately, we are throwing the “mutually” in there to try to clear up the possible confusion if we were to just use “exclusive”. Does this mean they only happen together? Or that they exclude each other? Making it “mutually exclusive” tries to clear this up. It works, as long as you don’t try to read too much into “mutually”.
Mutual = Together
Exclusive = Excluding the other item
I think the best way to dissect the phrase is:
The two items together [mutually] exclude/contradict each other [exclusive].
The phrase is usually used when talking about a sentence that doesn’t make sense because it is internally contradictory.
If I say “this room is too hot and too cold.”
then I have stated two things about the room:
1) it is too hot
2) it is too cold
Saying it’s too hot contradicts [excludes] saying it’s too cold.
Saying it’s too cold contradicts [excludes] saying it’s too hot.
Because you have put these two statements together [mutually], your whole statement about the room does not make sense.
It is a way of saying pick one or the other but not both. This is good for things that exist on a binary: On/off, heads/tails, bachelor/married, etc. Picking one excludes you from picking the other (Also works for things like a single dice, if you roll a one you can not have rolled any other number simultaneously).
In common English, this can sometimes just be the regular “or“. You can have ice cream OR you can have a hamburger (Implicit, pick one of them, you cannot have both). When you start talking about logic and Boolean logic, evaluating whether a proposition is true, an “OR” can be true if either statement is true.
“The children ate either spaghetti or dragons” is true if the children ate a bowl of spaghetti and is true if the children ate dragon-on-a-stick and is true if the children ate both a dragon and spaghetti; it is only a false statement if the children ate neither thing. In this example, mutually exclusive “or” (XOR) would be “The children ate spaghetti OR the children ate a dragon, but the children only ate one thing. In this case, it is true if and only if the children ate spaghetti or a dragon (but not both), and false if they did eat both, and false if they did not eat spaghetti OR dragon.
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