Exclusive we is a pronoun that indicates the speaker and perhaps other people, but excludes the addressee, as opposed to the inclusive we that includes the addressee. The English pronoun "we" is indeterminate in this parameter: the same word is used regardless of who's included. In linguistics and grammar, a pronoun is a pro-form that substitutes a noun or noun phrase with or without a determiner, such as you and they in English. ...
Exclusive or (usual symbol XOR occasionally EOR), which is sometimes called exclusivedisjunction, is a logical operator that results in true if one of the operands, but not both of them, is true.
The exclusivedisjunction of propositions A and B is usually called A xor B, where "xor" stands for "exclusive or" and is pronounced "eks-or" or "zor".
Exclusive-or is sometimes used as a simple mixing function in cryptography, for example, with one-time pad or Feistel network systems.
"Exclusivedisjunction is the sense of the word or as in the proverb you can have your cake or eat it (but not both)."
which is not supported by the definition of exclusivedisjunction.
In other words, if the meaning in the proverb were really the exclusivedisjunction, it would follow that I had permission to take one of the two actions, but you wouldn't tell me which.
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