logic and proof intro

For two binary events A and B, there are just 4 possible cases.

A	B
1	1
1	0
0	1
0	0

Chapter 1 - Negation.

There exists in the world the concept of negation, that is, the opposite. Not A is shown as $\neg$A.

A	B	$\neg$A	$\neg$B
1	1	0	0
1	0	0	1
0	1	1	0
0	0	1	1

Chapter 2 - Conjunctions.

	and	or
Symbol	$\wedge$	$\vee$
Expression	A $\wedge$ B	A $\vee$ B
Logic	True if both true, else false.	True if at least one trur, else false.

Below is the truth table.

A	B	A $\wedge$ B	A $\vee$ B
1	1	1	1
1	0	0	1
0	1	0	1
0	0	0	0

Chapter 3 - Statements.

	implication statement	equivalent statement
AKA	condition	bicondition
Symbol	$\to$	$\leftrightarrow$
Expression	A $\to$ B	A $\leftrightarrow$ B
Logic	If A then B.	If A then B. If not A then not B.
Pronunciation	If A then B. A implies B.	A is equivalent to B. A is true if and only if B is true.

Below is truth table.

A	B	A $\to$ B	A $\leftrightarrow$ B
1	1	1	1
1	0	0	0
0	1	1	0
0	0	1	1

Chapter 4 - Conjunctions and statements.

When the statements are combined with conjunctions, um. Good luck.

	implication statement	inverse statement	converse statement	negation conjunction	contrapositive statement
Logic	If A then B.	If not A then not B.	If B then A	A and not B	If not B then not A
Symbol	A $\to$ B	$\neg$A $\to$ $\neg$B	B $\to$ A	A $\wedge$ $\neg$B	$\neg$B $\to$ $\neg$A