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:
$$b\space∧\space c$$
but I am not certain.
You're right - $\wedge$ 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.