Complete the following patterns using conjectures.
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Directions: All of the statements below are FALSE. Since they are false, a counterexample needs to be given. For each statement, either list or illustrate an example and counterexample.
Statement Example Counterexample
All negative numbers are integers.
All fruit grows on trees.
All trees have leaves.
All fractions are positive.
All mammals have four legs.
All insects fly.
All lines are parallel.
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All quadrilaterals are squares.
Any three points are collinear.
All sea creatures have fins.
All polygons are quadrilaterals.
Any two angles are either complementary or supplementary.
All drinks are served cold.
All shoes have strings.
All restaurants have a drive-thru.
All movies have a happy ending.
All chairs have legs.
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All birds can fly.
All candy is sweet.
All books are boring.
All shirts have sleeves.
All flowers bloom.
All clocks have hands.
All boats have sails.
All locks have keys.
All blades are sharp.
All fans are for cooling.
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p: Parallel lines never intersect. q: Supplementary angles add up to 180 degrees. p and ~q: p and q:
~p^~q: p: The square root of 4 is 3. q: A triangle has 3 sides. r: January 1 is the first day of the year. p and r: p or ~q: q ^ r:
~q v r: p: 100 divided by 5 is 20. q: The midpoint of (0,0) and (2,4) is (1,1). p and q: p or q:
~p or q: p v ~q: p: Adjacent angles are beside each other.
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q: A 90 degree angle is obtuse. r:Vertical angles are congruent. p and r: p or r: p or q: q v r: q or ~r:
~p or q:
(p and r) or q:
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Episode Fun
-Episode Number:96 Season #3 First Aired: 5/17/54
After Lucy buys Ricky a set of golf clubs for their anniversary, the girls regret it when he and Fred become obsessed with the game.
Write out each conjunction or disjunction. Then state its final truth value. p: Lucy and Ethel take up basketball as a hobby. q: One thing the boys teach Lucy and Ethel is the “hop-skip-and-a-jump shot.” r: The pro-golfer that appears in this episode is Jimmy Woods.
1. p and q
2. ~p and r
3. ~r and p
4. ~p and ~q
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p: Lucy and Ethel take up basketball as a hobby. q: One thing the boys teach Lucy and Ethel is the “hop-skip-and-a-jump shot.” r: The pro-golfer that appears in this episode is Jimmy Woods.
5. p or r
6. ~p or r
7. ~q or p
8. ~q or ~r
9. (p and q) or r
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1. The Puzzle:
You are on an island and there are three crates of fruit that have washed up in front of you.
One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.
Each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges". You know that NONE of the crates have been labeled correctly - they are all wrong.
If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label
ALL of the crates correctly?
2. The Puzzle:
A man on a park bench is looking at a small portrait. You ask him, "Who is that in the picture?"
The man says, "Brothers and sisters, I have none, but that man's father, is my father's son."
Can you tell what person is in the picture?
3. The Puzzle: Three sisters are identical triplets. The oldest by minutes is Sarah, and Sarah always tells anyone the truth. The next oldest is Sue, and Sue always will tell anyone a lie. Sally is the youngest of the three.
She sometimes lies and sometimes tells the truth.
Victor, an old friend of the family's, came over one day and as usual he didn't know who was who, so he asked each of them one question.
Victor asked the sister that was sitting on the left, "Which sister is in the middle of you three?" and the answer he received was, "Oh, that's Sarah."
Victor then asked the sister in the middle, "What is your name?" The response given was, "I'm Sally."
Victor turned to the sister on the right, then asked, "Who is that in the middle?" The sister then replied, "She is
Sue."
This confused Victor; he had asked the same question three times and received three different answers.
Who was who?
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4. The Puzzle: Two fathers took their sons fishing.
Each man and son caught one fish, but when they returned to camp there were only 3 fish. How could this be?
(None of the fish were eaten, lost, or thrown back.)
5. The Puzzle:
A farmer wants to cross a river and take with him a wolf, a goat, and a cabbage. There is a boat that can fit himself plus either the wolf, the goat, or the cabbage. If the wolf and the goat are alone on one shore, the wolf will eat the goat. If the goat and the cabbage are alone on the shore, the goat will eat the cabbage.
How can the farmer bring the wolf, the goat, and the cabbage across the river?
6. The Puzzle: A Man carries his son into the hospital because his son has a nail in his foot. The Surgeon then walks in and says "I cannot operate on this boy … he is my son".
What is going on here?
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Puzzle 1. Four prisoners are arrested for a crime , but the jail is full and the jailer has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can go free but if they fail they are executed.
The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room).
He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats.
The prisoners can see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the men is allowed.
If any prisoner can figure out and say (out loud) to the jailer what color hat he has on his head all four prisoners
go free. How do the prisoners escape?
Puzzle 2. A black dog stands in the middle of an intersection in a town painted black. None of the street lights are working due to a power failure caused by a local storm. A car with two broken headlights drives towards the dog but turns in time to avoid hitting him. How could the driver have seen the dog in time?
Puzzle 3. Mike Peters was surprised to see his window slide open and was positively shocked when he saw two strangers climb inside. What transpired next could only be described as a despicable act of thievery. Mike watched with rapt fascination as the two thieves systematically began to remove the priceless Persian carpets, artwork, and jewelry. Having stripped the room, the thieves climbed back out the window. Incredibly, Mike went back to what he had been doing before the thieves arrived and soon he'd forgotten about the entire incident.
Why wouldn't Mike, who was in perfect health, have tried to stop the thieves or at the very least call the police after they had left?
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Puzzle 4.
How many times does the letter "F" appear in the statement to the left?
Puzzle 5. On the road to St. Vies, I met a man with seven wives. Each wife had seven sacks. Each sack had seven cats. Each cat had seven rats. How many were going to St. Vies?
Puzzle 6. Using only 3 and 5 gallon unmarked containers, place exactly 4 gallons of water on a scale to disarm a bomb.
Puzzle 7.
If teapot A holds 32 ounces of tea, about how many ounces does teapot B hold?
Puzzle 8. Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat. How?
Puzzle 9. A man is stranded on an island covered in forest. One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process. There are cliffs around the island, so he cannot jump off. How can the man survive the fire? (There are no buckets or any other means to put out the fire)
Puzzle 10. In the middle of an otherwise empty field there lies a man wearing a pack. He is dead. There are no other clues visible. How did he die?
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Puzzle 1.
Frank leaves home. When he tries to return, a man wearing a mask blocks his path.
1.) What is Frank doing?
2.) What is the masked man's occupation?
3.) Where is Frank's "safe place?"
Puzzle 2.
A woman is seated and is writing. There is a thunderstorm outside and she dies as a consequence. How did she die?
Puzzle 3.
A man was walking along a railway track when he spotted an express train speeding towards him. To avoid it, he jumped off the track, but before he jumped he ran ten feet towards the train.
Why?
Puzzle 4.
A man and his son were traveling on a scheduled flight across the Atlantic. The man asked the flight attendant if his son could have a look inside the cockpit. The boy was allowed to do this and the pilot gladly explained about the plane and its controls. After the boy left, the pilot turned to the co-pilot and said to him, "That was my son."
How could that be?
Puzzle 5.
A man is dead in a puddle of blood and water on the floor of a locked windowless room. What happened?
Puzzle 6.
What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?
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Puzzle 7.
LOGIC POEM:
The following verse spells out a word, letter by letter. "My first" refers to the word's first letter, and so on.
What's the word that this verse describes?
My first is in fish but not in snail
My second in rabbit but not in tail
My third in up but not down
My fourth in tiara not in crown
My fifth in tree you plainly see
My whole a food for you and me
Puzzle 8.
How is it possible to cut a traditional circular cake into 8 equal size pieces, with only 3 cuts?
Puzzle 9.
Using six contiguous straight lines, connect all of the sixteen circles shown below.
Puzzle 10.
Remove six matches to make ten.
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Answer the following questions using Venn diagrams.
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(Sung to the tune of: Twinkle, Twinkle Little Star)
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Directions: Find at least 5 examples of conditionals in advertising. After you find 5, paste them on this sheet, write each ad in if-then form, and then write the converse, inverse, and contrapositive of each.
Conditional:
Converse:
Inverse:
Contrapositive:
Conditional:
Converse:
Inverse:
Contrapositive:
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Conditional:
Converse:
Inverse:
Contrapositive:
Conditional:
Converse:
Inverse:
Contrapositive:
Conditional:
Converse:
Inverse:
Contrapositive:
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Write 4 statements using the Law of Detachment, then 4 statements using the Law of Syllogism.
1.
3.
5.
7. 8.
6.
4.
2.
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Discuss
After listening to the story “If You Give a Mouse a Cookie”, think about how this story is a real world example of the Law of Syllogism we have learned in class. Write the similarities below…
Now, write your own “Syllogism Story”
The story must be uniquely and appropriately written. The story must have at least 10 sentences. You must use correct spelling, punctuation, and sentence structure to receive a good grade. Brainstorm and pre-write your story on the back of this sheet.
Some ideas to think about…
 If you give a dog a danish…
 If you give a bear a biscuit…
 If you give a chimp a cheesecake…
Your grade will be based on the following criteria:
 Your story must apply to the Law of Syllogism
 Your story must be creative
 Your story must be 8 sentences
 You must use correct spelling, punctuation, and sentence structure
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1.
If you give a __________________________ a ___________________________, then ____________________________________________________________________________________.
2.
If ____________________________________________________________________________________, then _____________________________________________________________________________________.
3.
If ____________________________________________________________________________________, then _____________________________________________________________________________________.
4.
If ____________________________________________________________________________________, then _____________________________________________________________________________________.
5.
If ____________________________________________________________________________________, then _____________________________________________________________________________________.
6.
If ____________________________________________________________________________________, then _____________________________________________________________________________________.
7.
If ____________________________________________________________________________________, then _____________________________________________________________________________________.
8.
And chances are if_______________________________________________________________________, then _____________________________________________________________________________________.
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