Conditional Statements
Other Definitions
Direct Proof
Indirect Proof
Postulates and Theorems
100
What is a conditional statement?
A statement that has a hypothesis and a conclusion or IF and THEN parts.
100
What is the converse of a statement?
Interchanging the hypothesis and the conclusion.
eg. a->b, the converse is b->a
100
What is a direct proof?
Using a syllogism to prove a statement true.
100
What is an indirect proof?
Where an initial assumption leads to a contradiction.
100
What is the difference between a postulate and a theorem?
A postulate is considered true without a proof. A theorem is proven true with a proof
200
Draw an Euler Diagram for the following conditional statement
a->b
200
What does IFF mean?
If and only if. also the converse is true
eg. a->b = if a then b
a<->b if and only if a then b
200
What is syllogism?
Grouping statements together based on their if and then statements to prove something.
eg. a->b, b->c, a->c
200
What is a contradiction?
where a statement is proved false
200
A tripod is a device used to provide steady support to a camera. State the postulate that is the basis for the fact that a tripod has three legs.
Three non-colinear points define a plane.
300
What is a hypothesis, and what is a conclusion?
A hypothesis is the IF statement and a conclusion is the THEN statement
300
Is the converse of a statement always true?
When is it true?
Not always. Only when it is an IFF statement. eg. definition
300
Construct an Euler diagram for the following syllogism.
a->b, d->c, b->d
[a[b[d[c]]]]
300
What is the contradiction to the following statement?
a is not true
a is true
300
In the figure below, squares have been drawn on the sides of a right triangle.
Given that a=12 and b=16, find the area of all of the squares
c = 20
The squares are 144, 256, and 400
400
What is the hypothesis and conclusion of the following statement?
If at first you don't succeed, try, try again.
Hypothesis - If at first you don't succeed.
Conclusion - Then you try try again
400
What is the converse of the following statement? Is it true?
If Henry says I'm peeing! Then he needs to go potty.
If Henry needs to go potty. Then he says I'm peeing!
400
What premises are missing from the following proof?
1) If you give a mouse a cookie, then he is going to ask for a glass of milk.
[Premise 2]
3) If he wants a napkin, then he is going to want to look in the mirror to see if he has a milk moustache.
[Premise 4]
5) If he notices he needs a haircut, he is going to ask for a pair of scissors.
2) If he asks for a glass of milk, then he is going to want a napkin.
4) If he looks in the mirror, he is going to see he needs a haircut.
400
Prove 2x + 4 ≠ 12 indirectly with the following statement x= 5
(First assumption)
(Premise)
(Conclusion)
Assume 2x+4=12
Algebraically, that gives x=4
x=5 and not 4
Therefore
2x + 4 ≠ 12
400
With the figure below, find each of the following.
angleABC
x
angleBMC
x=50
angleABC = 100
angleBMC = 98
500
What is the hypothesis and conclusion of the following statement?
Failing to plan is planning to fail
-Benjamin Franklin
Hypothesis - If you fail to plan
Conclusion - Then you plan to fail
500
Write a IFF statement
If and only if a then b. A definition is a good example.
500
Please rewrite the following into IF and THEN format and arrange it logically. Then write the conclusion
A Panda would shoot the waiter if he took out a gun
If a Panda went to a restaurant, he would have a sandwich
If the panda leaves without paying then the panda eats shoots and leaves
A panda would take out a gun if he has a sandwich
if a panda shoots the waiter, then he would leave without paying
If a panda went to a restaurant, then he would have a sandwich
If he has a sandwich, then he would take out a gun
If he took out a gun, he would shoot the waiter
If he shot the waiter, then he would leave without paying
If a panda enters a restaurant, he would leave without paying.
If a panda enters a restaurant, then he eats, shoots, and leaves.
500
Mr. Boddy has been the victim of foul play. It happened after 4 p.m. After studying the relations of the statements given in the following proof, write the missing statements.
Theorem: Colonel Mustard did it.
Proof.
(What is the beggining assumption?)
If Colonel Mustard didn't do it, then Miss Scarlet did it.
(What statment belongs here?)
If it was done in the dining room, then it happened before noon.
(what does this contradict?)
Therefore, our assumption is false and
(what conclusion follows?)
Colonel Mustard didn't do it.
If Miss Scarlet did it, then it was done in the dining room.
contradicts that the murder happened at 4pm.
Colonel Mustard did it!!
500
You have the picture below.
What is the fraction of the perimeter of the square to the circumference of the circle?
What is the fraction of the area of the square to the area of the circle?
4/pi
4/pi