U2C2: Using Deductive Reasoning

Question 1

law of detachment

Answer 1

the law of logic that states that if the hypothesis of a true conditional statement is true, then the conclusion is also true

ex. if it is the weekend, then you do not attend school.
today is saturday.
saturday is part of the weekend, so the hypothesis is true, which means that the conclusion is also true. therefore, i will not attend school today.

Question 2

law of syllogism

Answer 2

the law of logic that states that if p -> q and q -> r are true, then p -> r is true

ex. all flooks are fleeks. all fleeks have red beaks.
it is a flook -> it is a fleek -> it has a red beak
thus, if it is a flook, then it has a red beak.
all flooks have red beaks.

Question 3

reflexive property

Answer 3

a = a

Question 4

symmetric property

Answer 4

if a = b, then b = a

Question 5

transitive property

Answer 5

if a = b and b = c, then a = c

Question 6

substitution property

Answer 6

if a = b and c + a = d, then c + b = d

Question 7

distributive property

Answer 7

if you have a, b, and c, then a(b + c) = ab + ac

Question 8

what types of facts can you use to solve an algebraic equation using deductive reasoning?

Answer 8

1. the hypothesis of a conditional statement
2. any known property
3. any statement that has been made previously in the problem