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Lets say I have something like this:

Define the propositional variable:

• b : Joe has maintained a B average.

• c : Joe has received below a C in a class.

• h : Joe is eligible for the honors program.

Translate the following sentence into logical propositions. For example the statement: ”If Joe has maintained an B average, then he is eligible for the honors program” would be translated as b → h .

Joe has maintained a B average even though he did receive a grade below a C in a class.

How does the 'even though' translate into logic? I think that it would be and ∧ and so the expression would be:

b ∧ c

but I am not certain.

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You're right - ∧ is the correct interpretation. English statements such as "even though", "however", "but", and "yet" all have usages that contrast facts, but they are all translated to "and" in propositional logic.

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  • Exactly, their use is retorical. Logically, they are just conjunctions Commented Oct 8, 2017 at 7:00
  • What would be some "English" words that equate to "OR" in logic? Or is this a thing we only have for "AND" ? Commented Aug 7, 2018 at 3:14

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