Logic for Contemporary Math

What is a disjunctive syllogism?

• A logical argument where one of the premises is a disjunction and the other premise negates one of the disjuncts, leading to the conclusion that the other disjunct must be true.

• A type of fallacy where the conclusion does not logically follow from the premises.

• A rhetorical device used to persuade an audience by appealing to their emotions.

• A mathematical theorem used to solve complex equations.

Consider the following argument: If Katja worked hard in the class, then she received a good grade in the class. Katja received a good grade in the class. Conclusion: Katja worked hard in the class. What fallacy does this argument represent?

• Affirming the Consequent

• Denying the Antecedent

• Begging the Question

• False Dilemma

The fallacy of the converse is:

• A logical error where the converse of a true statement is assumed to be true

• A type of argument that is always valid

• A method of proving mathematical theorems

• A rhetorical device used in speeches

What is the fallacy of the inverse?

• A logical error where the inverse of a conditional statement is assumed to be true

• A type of argument that attacks the person instead of the argument

• A reasoning that assumes a cause and effect relationship without evidence

• A fallacy that involves circular reasoning

What is a straw man argument?

• A type of logical fallacy where an opponent's argument is misrepresented to make it easier to attack

• A strong and valid argument that is difficult to refute

• An argument that is based on statistical evidence

• A type of argument that relies on emotional appeal rather than facts

What is the straw man fallacy?

• A type of argument that misrepresents an opponent's position

• A fallacy that involves attacking the person instead of the argument

• A logical fallacy that involves circular reasoning

• A fallacy that involves appealing to authority

What is the post hoc fallacy?

• A logical fallacy where one assumes that if one event occurs after another, then the first event must have caused the second.

• A fallacy that involves attacking the person making an argument rather than the argument itself.

• A fallacy that involves drawing a conclusion based on insufficient evidence.

• A fallacy that involves assuming that a small sample size is representative of a larger population.

What is Boolean logic?

• A type of algebra dealing with true or false values

• A programming language

• A type of hardware

• A mathematical theorem

A conditional statement is:

• a statement that performs a specific task

• a statement that evaluates a condition and executes code based on the result

• a statement that defines a variable

• a statement that loops through a block of code

What is a universal quantifier?

• A symbol used in logic to indicate that a statement applies to all elements of a domain

• A mathematical operation that sums all elements

• A type of variable in programming

• A specific number in a sequence