Example

P1) Every Roman emperor before Constantine was a pagan.

P2) Julian was a Roman emperor.

C) Julian was a pagan.

Invalid. P2 says that Julian was a Roman emperor, but not that he ruled before Constantine. It would be possible for the premises to be true but the conclusion false, then, if Julian were a non-pagan Roman emperor after Constantine.

a P1) Constantine ruled Rome before Constantius. P2) Constantius ruled Rome before Julian.

C) Constantine ruled Rome before Julian.

b P1) The only just political systems are democracies. P2) Rome's political system was unjust.

C) Rome's political system was not a democracy.

c P1) Unless some historians have told lies, there were miracles during the first century. P2) Some historians have told lies.

C) There were no miracles during the first century.

d P1) The accident on Sunday at Cleever's junction was caused by the driver coming too fast down the hill.

C) Accidents at Cleever's junction are always caused by drivers coming too fast down the hill.

P1) If Constantius' professed Christianity was genuine, then history has represented him unfairly. P2) We can never know that Constantius' professed Christianity was not genuine.

C) History has represented Constantius unfairly.

P1) If Germanicus had not died at the German front, he would have become emperor.

P2) If Germanicus had become emperor, then Tiberius would not have become emperor.

P3) If Tiberius had not become emperor, then Caligula would not have become emperor.

P4) If Caligula had not become emperor, then he would not have been murdered.

P5) If Caligula had not been murdered, then Claudius would not have become emperor.

C) If Germanicus had not died at the German front, then Claudius would not have become emperor.

P1) If any Roman emperor was wise, then Marcus Aurelius was wise. P2) Augustus was a Roman emperor. P3) If Augustus was wise, then Marcus Aurelius was not wise.

C) Marcus Aurelius was wise.

Logic: deductive validity

h

P1)

If John and Susan are late, then Mary will be

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