Geo 2.1-2.3 Flashcard Part 1

Front

What is a conditional statement in logic?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, typically written as 'If p, then q' (symbolically: @@p ightarrow q@@).

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', symbolically represented as @@q ightarrow p@@.

Front

What is an inverse of a conditional statement?

Back

The inverse of a conditional statement 'If p, then q' is 'If not p, then not q', symbolically represented as @@ eg p ightarrow eg q@@.

Front

What is a contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If p, then q' is 'If not q, then not p', symbolically represented as @@ eg q ightarrow eg p@@.

Front

What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement, showing that it is not always true.

Front

What does it mean to prove a conjecture false?

Back

To prove a conjecture false means to provide a counterexample that demonstrates the conjecture does not hold in all cases.

Front

What is the difference between a conditional statement and its converse?

Back

A conditional statement asserts a relationship from p to q, while its converse asserts the relationship from q to p. They are not logically equivalent.

Front

What is the logical structure of a conditional statement?

Back

A conditional statement consists of two parts: the hypothesis (p) and the conclusion (q), structured as 'If p, then q'.

Front

How do you identify the hypothesis and conclusion in a conditional statement?

Back

In the statement 'If p, then q', 'p' is the hypothesis (the condition) and 'q' is the conclusion (the result).

Front

What is the symbolic representation of the inverse of @@p ightarrow q@@?

Back

The inverse is represented as @@ eg p ightarrow eg q@@.