Logical Deduction Flashcards

All judges are lawyers. Some lawyers are professors. Which conclusion must be true?

Answer: Some lawyers are judges

Since all judges are lawyers, it follows necessarily that some lawyers (namely, all judges) are judges.

If the defendant is acquitted, the prosecution will appeal. The prosecution did not appeal. What can we conclude?

Answer: The defendant was convicted

By modus tollens: if acquittal leads to appeal, and there was no appeal, then there was no acquittal — meaning the defendant was convicted.

In a group of 50 students, 30 study philosophy and 25 study history. What is the minimum number who study both?

Answer: 5

The minimum overlap is 30 + 25 − 50 = 5, by the inclusion-exclusion principle.

Every contract requires offer, acceptance, and consideration. This agreement has offer and acceptance but no consideration. What follows?

Answer: It is not a valid contract

Since a necessary condition (consideration) is absent, the agreement cannot be a valid contract.

Only barristers can appear in the Supreme Court. Sarah appeared in the Supreme Court. Therefore:

Answer: Sarah is a barrister

'Only barristers can appear' means appearing implies being a barrister, so Sarah must be a barrister.

If A testifies, B will be implicated. If B is implicated, C will resign. A testifies. What must follow?

Answer: C resigns

By chained modus ponens: A testifies → B implicated → C resigns.

No criminal acts are morally praiseworthy. Some courageous acts are criminal. Which statement is supported?

Answer: Some courageous acts are not morally praiseworthy

The courageous acts that are criminal cannot be morally praiseworthy, so some courageous acts are not morally praiseworthy.