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Description: If 'P implies Q' is true and 'Q' is false, then 'P' must also be false. Example: If the alarm is set (P), it will make a sound if an intruder comes (Q). The alarm did not make a sound. Therefore, the alarm was not set.

Description: Given two conditional statements 'P implies Q' and 'R implies S', if at least one of 'Q' or 'S' is false, then at least one of 'P' or 'R' is false. Example: If it's a weekday (P), I have to go to work (Q). If it's the weekend (R), I can sleep in (S). It's neither a weekday nor the weekend. Thus, I neither have to go to work nor can I sleep in.

Description: If 'P implies Q' and 'Q implies R' are both true, then 'P implies R' is also true. Example: If I exercise (P), I will burn calories (Q). If I burn calories (Q), I will lose weight (R). Hence, if I exercise (P), I will lose weight (R).

Description: Given two conditional statements 'P implies Q' and 'R implies S', if at least one of 'P' or 'R' is true, then at least one of 'Q' or 'S' is true. Example: If I study (P), I will pass (Q). If I relax (R), I will be happy (S). I am either studying or relaxing. Therefore, I will either pass or be happy.

Description: If 'P implies Q' is true and 'P' is true, then 'Q' must also be true. Example: If it is raining (P), the street will be wet (Q). It is raining. Therefore, the street is wet.

Description: If 'P or Q' is true and 'P' is false, then 'Q' must be true. Example: It is either snowing (P) or raining (Q). It is not snowing. Therefore, it is raining.

Description: If 'P implies Q' and 'Q implies P' are both true, then 'P if and only if Q' is true. Example: You can borrow my car if and only if you fill it with gas. It means if you fill it with gas, you can borrow my car, and if you are borrowing my car, you must have filled it with gas.