2.1 Practice B

Identify the Hypothesis and Conclusion of the following Conditional Statement:

If you like to eat, then you are a good cook.

• H: you like to eat

  C: you are a good cook

• H: you are a good cook

  C: you like to eat

Identify the Hypothesis and Conclusion of the following Conditional Statement:

If an animal is a bear, then it is a mammal.

• H: it is a mammal

  C: an animal is a bear

• H: an animal is a bear

  C: it is a mammal

Let p be “a tree is an oak tree” and let q be “it is a deciduous tree.” Write the conditional statement in words. Then decide whether it is true or false.

• If a tree is a deciduous tree, then it is an oak tree; True

• If a tree is an oak tree, then it is a deciduous tree; True

• If a tree is a deciduous tree, then it is an oak tree; False

• If a tree is an oak tree, then it is a deciduous tree; False

Let p be “a tree is an oak tree” and let q be “it is a deciduous tree.” Write the converse in words. Then decide whether it is true or false.

• If a tree is a deciduous tree, then it is an oak tree; True

• If a tree is an oak tree, then it is a deciduous tree; True

• If a tree is a deciduous tree, then it is an oak tree; False

• If a tree is an oak tree, then it is a deciduous tree; False

Let p be “a tree is an oak tree” and let q be “it is a deciduous tree.” Write the inverse in words. Then decide whether it is true or false.

• If a tree is not a deciduous tree, then it is not an oak tree; True

• If a tree is not an oak tree, then it is not a deciduous tree; True

• If a tree is not a deciduous tree, then it is not an oak tree; False

• If a tree is not an oak tree, then it is not a deciduous tree; False

Let p be “a tree is an oak tree” and let q be “it is a deciduous tree.” Write the contrapositive in words. Then decide whether it is true or false.

• If a tree is not a deciduous tree, then it is not an oak tree; True

• If a tree is not an oak tree, then it is not a deciduous tree; True

• If a tree is not a deciduous tree, then it is not an oak tree; False

• If a tree is not an oak tree, then it is not a deciduous tree; False

Decide whether the statement about the diagram is true or false

• True

• False

Decide whether the statement about the diagram is true or false

• True

• False

Rewrite the two statements as a single biconditional statement: A rectangle is a quadrilateral that has all perpendicular sides. If all sides of a quadrilateral are perpendicular, then it is a rectangle.

• If a quadrilateral is a rectangle, then it has all perpendicular sides

• If all sides of a quadrilateral are perpendicular, then it is a rectangle

• A quadrilateral is a rectangle if it has all perpendicular sides 

• A quadrilateral is a rectangle if and only if it has all perpendicular sides

Your friend claims that only true conditional statements have a true contrapositive.

• True

• False