Lesson 2-3Deductive Reasoning

Law of Detachment:If p ⇒ q is a true conditonal and p

is true, then q is true

ex: 1. If a vehicle is a car, then it has four wheels is a true conditional. Use the Law of Detachment to reach a valid conclusion.

2. Determine if a valid conclusion can be reached from the 2 true statements by the Law of Detachment. If a valid conclusion is possible, state it. 1) If I watch TV I will not do my

homework. 2) I did my homework.

3. If possible, use the Law of Detachment to draw a conclusion. If not possible write no conclusion.

a) 1) If a figure is a rectangle, then it has two pairs of parallel sides. 2) Figure ABCD is a rectangle.

b) 1) If n is a prime number greater than 2, then n2 is an odd number.

2) 92 is an odd number.

Law of Syllogism:If p ⇒q and q ⇒r are true

conditionals, then p ⇒r is true

ex.1. Determine if a valid conclusion can be reached from the two true statements using the law of syllogism.

1) If Elna takes the car to the store, she will stop at the post office.

2) If Elna stops at the post office, she will buy stamps.

2. Use the law of syllogism to draw a conclusion.

1) If two planes intersect , then they intersect

in a line.2) If two planes are not parallel then

theyintersect.

3. Determine if statement 3 follows from statements 1 and 2.

1) If fossil fuels are burned then acid rain is produced.

2) If acid rain is produced, wildlife suffers.3) If fossil fuels are burned, then wildlife

suffers.

4. Use the law of Detachment and the Law of Syllogism to draw conclusions from the following true statements.

1) If a river is more than 4000 mi long, then it

is longer than the Amazon.2) If a river is longer than the Amazon,

then if is the longest river in the world.

3) The Nile is 4132 mi long.

Use the law of Detachment and the Law of Syllogism to draw conclusions from the following true statements.

1) The Volga River is in Europe.2) If a river is less than 2300 mi long, it

is not one of the world's ten longest

rivers.3) If a river is in Europe, then it is less

than2300 mi long.