Unit 2 Flashcard

Front

What is a converse statement?

Back

A converse statement is formed by reversing the hypothesis and conclusion of a conditional statement. For example, the converse of 'If P, then Q' is 'If Q, then P.'

Front

Identify the hypothesis and conclusion in the statement: 'If it rains, then the ground is wet.'

Back

Hypothesis: It rains; Conclusion: The ground is wet.

Front

What is the conditional statement form?

Back

A conditional statement is typically expressed in the form 'If P, then Q,' where P is the hypothesis and Q is the conclusion.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' It is logically equivalent to the original statement.

Front

What does it mean for two statements to be logically equivalent?

Back

Two statements are logically equivalent if they have the same truth value in all possible scenarios.

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.'

Front

Provide an example of a converse statement.

Back

Original statement: 'If a shape is a square, then it has four sides.' Converse: 'If a shape has four sides, then it is a square.'

Front

What is a biconditional statement?

Back

A biconditional statement is a statement that combines a conditional and its converse, expressed as 'P if and only if Q.'

Front

How do you determine the truth value of a conditional statement?

Back

A conditional statement is false only when the hypothesis is true and the conclusion is false; otherwise, it is true.

Front

What is a necessary condition?

Back

A necessary condition is a condition that must be true for a statement to be true. In 'If P, then Q,' Q is a necessary condition for P.