Logic And Proof Techniques

Question 1

Define a statement
Aka…

Answer 1

A statement is a sentence that is either true or false but not both
Aka proposition

Question 2

What is a logical connective?

Answer 2

Logical connectives are used to combine simple statements into complex ones

Question 3

What is useful about or in mathematics?

Answer 3

It is inclusive so if P and Q are true
then P or Q is true

Question 4

Define conjunction

Answer 4

A statement that is true if both P and Q are true; otherwise it is false

Question 5

Define disjunction

Answer 5

A statement that is true if either one of P or Q is correct or both; otherwise it is false

Question 6

What is a truth table?

Answer 6

A table that shows the different possibilities if P and Q… are true or false

Question 7

Define negation

Answer 7

This statement is true if P is false and false if P is true

Question 8

Define implication

Answer 8

Question 9

What do you need to remember to make implications make sense?

Answer 9

We give the benefit of the doubt. If P is false then the implication is true

Question 10

What is one way to prove that 2 statements are equivalent?

Answer 10

Create their truth tables

Question 11

Define equivalence

Answer 11

Question 12

How do you abbreviate if and only if

Answer 12

Iff

Question 13

Give a useful implication example

Answer 13

The proposition if it rains then i bring an umbrella.
If you see an umbrella it doesn’t mean it isn’t raining

Question 14

How mnay laws of logic are there?

Answer 14

7

Question 15

State the first 3 laws of logic

Answer 15

Question 16

State the absorption laws of logic

Answer 16

Question 17

State the distributive laws

Answer 17

Question 18

State De Morgan’s laws

Answer 18

Question 19

State the law of syllogism

Answer 19

Question 20

What are the names of the different laws of logic?

Answer 20

Commutative
Associative
Idempotent
Absorption
Distributive
De Morgan’s
Law of Syllogism

Question 21

Negate the statement P implies Q

Answer 21

Question 22

What is a predicate

Answer 22

A predicate is a softer statement, usually when we haven’t defined what x is

Question 23

What do you need to be careful about quantifiers
+++

Answer 23

The order really matters (Proof of infinity example)

This is less important when the quantifiers are the same

Question 24

How can we prove a statement which gives x as being part of the finite set X?

Answer 24

Try all values or use an arbitrary value x and prove it

Question 25

How do you want to disprove the statement that looks like this:

Answer 25

Counterexample

Question 26

How do you prove a statement in the form of this:

Answer 26

Give 1 answer which fulfils the equation

Question 27

What is a comon way to prove/ disprove statements?

Answer 27

Disprove/prove their negations

Question 28

What do i keep forgetting about he E symbol?

Answer 28

It means exists 1
1
So i can choose the value i use in the domain

Question 29

What is te contrapositive

Answer 29

Question 30

What is the converse?

Answer 30

Question 31

Hat is the point of proof by contradiction?

Answer 31

If we can negate our statement and assume is true then we can get some absurd thing such as 1=2 then our assumption must be false

Question 32

What will help me when doing negations?

Answer 32

Translate the words into symbols then negate it

Question 33

What can we use contrapositives to our advantage?

Answer 33

If we can prove the contrapositive true that means that he original implication is true as implication is equivalent to contrapositive

Question 34

What is a common technique when proving inequalities?

Answer 34

Using our brain and saying that this has to be at least less than n etc

Question 35

How is the contrapositive of an implication useful to us?

Answer 35

They are the same thing so proof of either is proof of the implication