BOOLEAN ALGEBRA.pptx.................................

BOOLEAN ALGEBRA.pptx.................................

• 1.
  BOOLEAN ALGEBRA LOGIC GATES
• 2.
  WHAT IS BOOLEANALGEBRA?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  THEPROPOTIONAL 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  Acompound 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 (Ifand 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 ONLYIF /BI CONDITIONAL) | A | B | A ↔ B | ----------------------------- | 0 | 0 | 1 |K | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |
• 17.
  EQUIVALENCE PROPOTIONAL LAWS