Logic is a symbolic language. It is also a very precise language, every term well defined and unambiguous. English, on the other hand, is a somewhat ambiguous language. The same word can have multiple meanings: a pen is a writing utensil and an enclosure for livestock.
One key term in logic is the disjunction “or”. In English, the word “or” has two meanings. The first is the inclusive or, which means basically “this, or that, or both.” If someone said, “Most Bible students read the King James or the NIV,” this statement is still true for a student who reads both the King James and the NIV. The “or” includes both possibilities.
The exclusive or basically means “this or that, but not both.” This is the sense used in this classic argument for the deity of Christ: “Jesus was either God or a bad man.” If Jesus was God, then He was not a bad man. If He was a bad man, then He was not God.
Symbolic logic deals with the ambiguous “or” this way. The logical operator OR is taken in the inclusive sense. “A or B” is true if A is true, B is true, or both A and B are true. To represent the exclusive or, we use the compound proposition “A or B, but not both A and B.”