For each of these sentences, state what the sentence means...

For each of these sentences, state what the sentence means if the logical connective or is an inclusive or (that is, a disjunction) versus an exclusive or. Which of these meanings of or do you think is intended? a) To take discrete mathematics, you must have taken calculus or a course in computer science. b) When you buy a new car from Acme Motor Company, you get $\$ 2000$ back in cash or a $2 \%$ car loan. c) Dinner for two includes two items from column A or three items from column $\mathrm{B}$. d) School is closed if more than 2 feet of snow falls or if the wind chill is below $-100$.

For each of these sentences, state what the sentence means if the logical connective or is an inclusive or (that is, a disjunction) versus an exclusive or. Which of these meanings of or do you think is intended?
a) To take discrete mathematics, you must have taken calculus or a course in computer science.
b) When you buy a new car from Acme Motor Company, you get $\$ 2000$ back in cash or a $2 \%$ car loan.
c) Dinner for two includes two items from column A or three items from column $\mathrm{B}$.
d) School is closed if more than 2 feet of snow falls or if the wind chill is below $-100$.

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Key Concepts

Inclusive Or

This concept refers to a logical disjunction in which one or both of the statements can be true. In other words, an inclusive 'or' is true if either or both propositions are true. It is the standard interpretation in most logical and mathematical contexts, where the connective does not exclude the simultaneous truth of both operands.

Exclusive Or

Exclusive or (often abbreviated as XOR) is a logical connective which holds true only when exactly one of the propositions is true, but not both. This means that if both propositions are true, the exclusive 'or' would be false. It is used to represent choices or conditions where the simultaneous truth of both options is not allowed or desired.

Interpretation of Logical Connectives in Natural Language

Natural language often contains ambiguity when using words like 'or', and it becomes important to determine whether a speaker means the inclusive or exclusive sense. The context surrounding the statement, as well as common usage in that domain, can provide clues to the intended meaning, making this concept essential in translating everyday language into formal logic.

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