12th computer

1. BOOLEAN ALGEBRA
LOGIC GATES

2. WHAT IS BOOLEAN ALGEBRA?M
 Boolean algebra is a type of math that deals with true and false values,
often represented as 1 and 0. It's named after a mathematician named
George Boole. This type of math is really important in computer science
and electronics because computers work with binary code, which is made
up of just ones and zeros.

3. PROPOTIONAL LOGIC
 THE PROPOTIONAL LOGIC REPRESENTS LOGIG THROUGH PROPOSITIONS
AND LOGICAL CONNECTIVES.PROPOTION AS AN ELEMENTARY ATOMIC
SENTENCE THAT MAY TAKE EITHER TRUE OR FALSE VALUE BUT MAY NOT
TAKE ANY OTHER VALUE
 (AKA :- it can only take true or false value )
Example :-
 It is raining (It is proposition as it may either be true or false )
 Taylor swift is not cringe (It is also a proposition as it is false )
 Kanye west is better than Taylor swift (It Is also proposition as it is true)

4. A SIMPLE PROPOSITION
 A simple proposition is a basic statement that can be either true or false,
but not both. It's a statement that doesn't contain any other statements
within it.
Here are some examples of simple propositions:
 "The sky is blue." (This is either true or false, depending on the current
weather and time of day.)
 "2 + 2 = 4." (This is a mathematical statement that is always true.)

5. COMPOUND PROPOSITION
 A compound proposition is a statement formed by combining two or
more simple propositions using logical operators. These logical operators
include "and" (conjunction), "or" (disjunction), "not" (negation), "if...then"
(implication), and "if and only if" (biconditional).
Let's break down each of these:

6. DISJUNCTIVE (OR)
 Disjunction (Or): denoted by "∨". It combines two simple propositions
and is true when at least one of the individual propositions is true. For
example, if "A" is "It is raining" and "B" is "It is snowing", then "A ∨ B"
means "It is raining or snowing".

7. CONJUCTIVE (AND)
 Conjunction (And): denoted by "∧". It combines two simple propositions
and is true only when both of the individual propositions are true. For
example, if "A" is the proposition "It is sunny" and "B" is the proposition "It
is warm", then "A ∧ B" means "It is sunny and warm".

8. CONDITIONAL
 Conditional (If...Then): denoted by "→". It's like making a promise. In an
conditional "A → B", A is called the antecedent (the "if" part) and B is
called the consequent (the "then" part). The statement is false only when
the antecedent is true and the consequent is false. For example, "If it is
raining, then I will take an umbrella".

9. BICONDITIONAL
 Biconditional (If and Only If): denoted by "↔". It's a statement that
asserts that two propositions are both true or both false. For example, "A
↔ B" means "A if and only if B", which implies that A and B have the same
truth value.

10. NEGATION
 Negation (Not): denoted by "¬". It's used to reverse the truth value of a
proposition. For example, if "A" is "It is cold", then "¬A" means "It is not
cold", which is true when it's not cold.

11. TRUTH TABLE

12. 1) NEGATION (NOT)
|A| |¬A|
-----------------
| 0 | | 1 |
| 1 | | 0 |

13. 2) DISJUNCTION (OR)
| A | B | A ∨ B |
-----------------------------
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

14. 3)CONJUNCTION(AND)
| A | B | A ∧ B |
-----------------------------
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

15. 4)IMPLICATION(IF……………..THEN/CON
DITIONAL)
| A | B | A → B |
------------------------------
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

16. 5)EQUIVALENCE(IF AND ONLY IF /BI
CONDITIONAL)
| A | B | A ↔ B |
-----------------------------
| 0 | 0 | 1 |K
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

17. EQUIVALENCE PROPOTIONAL LAWS