WARM UP
1. Write a two column proof for the following problem:
Given: 𝑥+5
=5
4
Prove: x=15
2. If possible, write the bi-conditional form of the statement below:
Palm trees grow in warm climates

ANNOUNCEMENTS
• Test Thursday!
• Homework
1.Pg: 62-63 #’s 1-4 & 6-11
2.Work on review to study for Test on
Thursday

WHAT CAN WE CONCLUDE???
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DEDUCTIVE REASONING
• The process of using logic to get from what you know is true to new conclusions
• If the statements are true (what you know) what you conclude will also be true

TYPE ONE
• If Mrs. Hendricks is hungry then she is grumpy
• Mrs. Hendricks is hungry
• What can we conclude???

LAW OF DETACHMENT
If a conditional statement its true, and its hypothesis is true, then its conclusion will be true as well.
Symbolic form:
If p→q is a true statement and p is true then q is true
**→ means if then statement

TYPE TWO
• If it rains the flowers will grow
• If the flowers grow Mrs. Hendricks will be happy
THEREFORE
• If it rains Mrs. Hendricks will be __________
WHAT DID WE DO???
What do you notice about the first two conditional statements?

LAW OF SYLLOGISM
Allows you to state one conclusion from 2 true conditional statements when the conclusion from one statement is the hypothesis from the other statement.
Symbolic Form:
If p→q and q→r are true statements, then p→r is a true statement
**→ means if then statement

MIND PUZZLES
Who killed Colonel Mustard?
Things you know:
• If someone was in the lounge, then they were the perpetrator that killed
Colonel Mustard
• If professor plum was in the kitchen then Miss Peacock was in the library
• If Ms. Peacock was in the library then Miss Scarlet was in the lounge
• If Ms. Peacock was in the lavatory then Mr. White was in the lounge
• If Mr. Green was hungry, then Mr. Plum would make him sandwich in the kitchen
• Mr. Green was hungry

Who Took The Candy Bar?
During the lunch hour at school, a group of five boys from
Miss Jones home room visited a nearby lunch wagon. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:
1. Rex: "Neither Earl nor I did it."
2. Jack: "It was Rex or Abe."
3. Abe: "Both Rex and Jack are lying."
4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."
5. Earl: "What Dan said is wrong."
When Miss Jones was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Jones is correct, can you determine who took the candy bar?

HOMEWORK
1.Pg: 62-63 #’s 1-4 & 6-11
2.Work on review to Study for Test on
Thursday