Converse, Inverse, Contrapositive

What is the relationship between a statement and its contrapositive?

• A statement and its contrapositive are logically equivalent; if one is true, the other is also true.

• A statement and its contrapositive are always false together.

• A statement and its contrapositive can never be true at the same time.

• A statement and its contrapositive are unrelated and independent.

What is the converse of a conditional statement?

• The converse of a conditional statement is 'If P, then Q'.

• The converse of a conditional statement is 'If Q, then P'.

• The converse of a conditional statement is 'If not P, then not Q'.

• The converse of a conditional statement is 'If Q, then not P'.

What is the difference between a converse and an inverse?

• The converse switches the hypothesis and conclusion, while the inverse negates both the hypothesis and conclusion.

• The converse negates the hypothesis and conclusion, while the inverse switches them.

• The converse is the same as the inverse, just with different terminology.

• The converse only applies to conditional statements, while the inverse applies to all types of statements.

What is a conditional statement?

• A statement that can be true or false depending on the situation.

• A logical statement that has two parts: a hypothesis (if part) and a conclusion (then part).

• A statement that only expresses a fact without any conditions.

• A type of statement that is always true regardless of circumstances.

Given the statement 'If an angle is obtuse, then it is greater than 90 degrees', what is the contrapositive?

• If an angle is not greater than 90 degrees, then it is not obtuse.

• If an angle is less than 90 degrees, then it is acute.

• If an angle is greater than 90 degrees, then it is obtuse.

• If an angle is not obtuse, then it is less than or equal to 90 degrees.

What is the inverse of a conditional statement?

• If P, then Q

• If not P, then not Q

• If Q, then P

• If not Q, then not P

What is the definition of a hypothesis in a conditional statement?

• The hypothesis is the 'if' part of a conditional statement, representing the condition that must be true for the conclusion to follow.

• The hypothesis is the 'then' part of a conditional statement, representing the outcome that follows the condition.

• The hypothesis is a statement that can be proven true or false, independent of any conditions.

• The hypothesis is a general assumption made without evidence, often used in scientific reasoning.

If Jenny buys a guitar, then she will not buy a keyboard. What is the contrapositive?

• If Jenny buys a keyboard, then she will not buy a guitar.

• If Jenny does not buy a guitar, then she will buy a keyboard.

• If Jenny does not buy a keyboard, then she will buy a guitar.

• If Jenny does not buy a guitar, then she will not buy a keyboard.

What does it mean if a conclusion is valid?

• A conclusion is valid if it logically follows from the premises or statements given.

• A conclusion is valid if it is widely accepted by the majority.

• A conclusion is valid if it is based on personal opinion.

• A conclusion is valid if it is stated in a formal document.

Given the statement 'If I am hungry, then I eat', what is the inverse?

• If I am not hungry, then I don't eat.

• If I eat, then I am hungry.

• If I am hungry, then I don't eat.

• If I don't eat, then I am not hungry.