Logic-Geometry

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or proposition. For instance, the statement 'All fractions are between 0 and 1' can be disproven by the counterexample 3/2.

Front

What is deductive reasoning?

Back

Deductive reasoning is a logical process where a conclusion is reached based on the concordance of multiple premises that are generally assumed to be true. For example, 'All bears are mammals; all mammals have kidneys; therefore, all bears have kidneys.'

Front

What is the inverse of a conditional statement?

Back

The inverse of a conditional statement 'If p, then q' is 'If not p, then not q.' For example, the inverse of 'If it does not rain today, then we will have practice' is 'If it rains today, then we will not have practice.'

Front

What is a contrapositive?

Back

The contrapositive of a conditional statement 'If p, then q' is 'If not q, then not p.' For example, the contrapositive of 'If I have a Siberian Husky, then I have a dog' is 'If I do not have a dog, then I do not have a Siberian Husky.'

Front

What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r', then 'p implies r'. For example, if 'If it rains, then the ground is wet' and 'If the ground is wet, then the grass is wet', then 'If it rains, then the grass is wet.'

Front

What is an example of an inductive reasoning?

Back

Inductive reasoning involves making generalizations based on specific observations. For example, observing that the sun rises in the east every day and concluding that the sun always rises in the east.

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions. For example, 'If it rains, then the ground will be wet.'

Front

What is the converse of a conditional statement?

Back

The converse of a conditional statement 'If p, then q' is 'If q, then p.' For example, the converse of 'If it rains, then the ground is wet' is 'If the ground is wet, then it rains.'

Front

What is negation in logic?

Back

Negation is the logical operation that takes a proposition and flips its truth value. For example, the negation of 'It is raining' is 'It is not raining.'

Front

What is a logical fallacy?

Back

A logical fallacy is an error in reasoning that renders an argument invalid. For example, 'If we allow students to redo tests, soon they will expect to redo all assignments.'