Laws of Logic

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

(1) If you have a can opener, you can open a can.
(2) Jon has a can opener.
(3) John can open a can.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Syllogism
• Law of Detachment
• Law of Syllogism
• invalid

If a mineral is gypsum, it has a hardness of 2.
If a mineral has a hardness of 2, it can be scratched with a fingernail.
Using the Law of Syllogism, what logically comes next?

• If a mineral can be scratched with a fingernail, then it is gypsum.
• If a mineral is gypsum, it can be scratched with a fingernail.
• If a mineral has a hardness of 2, then it can't be scratched with anything.
• It can be scratched with a fingernail.

If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?

• ∠A is complementary to ∠B
• ∠A is acute.
• ∠A is obtuse.
• ∠A is 40⁰

Tags

CCSS.HSG.CO.A.1

(1)  If it is a rabbit, then it has long ears.
(2)  Peter Cottontail has long ears.
(3)  Peter Cottontail is a rabbit.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• invalid

(1) If you drive safely, then the life you save may be your own.
(2) AJ drives safely.
(3)  The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Detachment
• Law of Syllogism
• Law of Contrapositive
• invalid

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?

• Figure A is a polygon.
• Figure A is a circle.
• Figure A is a square.
• invalid; nothing belongs in line 3

Tags

CCSS.2.G.A.1

Using the Law of Detachment, what can you conclude?
If you earn more than $14, then you can buy a new CD.
You earn $15.

• you can buy a new CD
• you cannot buy a new CD
• no conclusion can be made
• you earn more than $14

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Use Law of Syllogism to make a conclusion.
If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
If the length of a side of a square is 5 ft, then the area is 25 ft².

• If the side of a square is 5 ft, then the perimeter is 20 ft.
• If the perimeter of a square is 20 ft, then the area is 25 ft²
• If the area of a square is 25 ft², then the side length is 5 ft. 
• If the are of a square is 25 ft², then the perimeter is 20 ft.

Tags

CCSS.HSA.SSE.A.1