Ch.2 conditional statements

Question 1

If and then statements have

Answer 1

Cause and effect

Question 2

Conditional statement:

Answer 2

A logical statement that has 2 parts, HYPOTHESIS AND CONCLUSION.
- hypothesis (if)
- conclusion (then)
- if (p)
- then (Q)
- example: if an animal is a bird, then it has feather
- NOT ALWAYS TRUE

Question 3

Hypothesis:

Answer 3

Prediction

Question 4

Negation

Answer 4

Opposite of the original statement
Add not to condition statement
Example: the ball is NOT red

Question 5

Converse

Answer 5

• Skaters wear Converses and they FLIP on skateboards
• CONCLUSION THEN HYPOTHESIS

Question 6

Inverse

Answer 6

Negate p,Q
- add not to if and then
- add not to conditional statements

Question 7

Contrapositive

Answer 7

Negate and flip the hypothesis and conclusion
- if not Q, then not p

Question 8

Symbols

Answer 8

• hypothesis ( P)
• conclusion ( Q)
  —-> for if,then
  ~ negation

Question 9

Equivalent statement

Answer 9

When two statements are both true and false

Question 10

Conjecture:

Answer 10

An unproven statement based on observations
Example: the sum of two numbers is always more then the greater number

Question 11

Inductive reasoning

Answer 11

When you find a pattern and specific examples then you write a conjecture based off of it.

Question 12

How to use inductive reasoning

Answer 12

1.Make observations and gather data
2. Look at your data and search for patterns
3. Make conclusions/theories

Question 13

Deductive reasoning

Answer 13

Uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

Question 14

Counterexample

Answer 14

Evidence that shows that the conjecture is false

Question 15

Counterexample=

Answer 15

The conjecture is false

Question 16

Laws of logic

Answer 16

Law of detachment: if the hypothesis of a true conditional statement is true,then the conclusion is also true
Law of syllogism: a logical pattern that can be used to reach a conclusion based on two statements