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Title: propositional logic gates
Description: Propositional logic uses statements (propositions) that are either true or false. Logic gates are physical or virtual devices that implement Boolean functions—the same kind of logic that propositional logic uses. So, propositional logic gates are electronic representations of logical operations (such as AND, OR, NOT) on propositions.
Description: Propositional logic uses statements (propositions) that are either true or false. Logic gates are physical or virtual devices that implement Boolean functions—the same kind of logic that propositional logic uses. So, propositional logic gates are electronic representations of logical operations (such as AND, OR, NOT) on propositions.
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Propositional logic:
A fundamental concept in computer science
...
Truth tables is a method for determining the truth
value of complex logical formulas
...
Logical operators like AND, OR, NOT, XOR, implication, and biconditional are used to
combine and modify propositions
...
Example:
1
...
1+3=5
Therefore,1 is true & 2 is false this is a propositional
The statements have two types:
1
...
Molecular statement or compound statement
1
...
Eg: 1
...
Tamil is a language and Chennai is the capital of Tamilnadu
Logic:
Logic is fundamental to computers, dictating their actions based on true or false
statements
...
Computer scientists use formal logical systems, such as propositional
logic, to express ideas about statements and their truth values with precision
...
A proposition, such as "The robot is blue," can be represented by a
variable like 'P'
...
Combining and
modifying these logical variables creates more complex logical formulas
...
If P represents "The robot is
blue," then "not P" (represented by ¬P) is true when the robot is not blue
...
p
T
F
It is a unary operator
¬P
F
T
Conjunction (And):
Conjunction, or "and" (represented by ∧), combines two logical formulas and is true
only if both formulas are true
...
Truth Table
P
T
T
F
F
Q
T
F
T
F
P^Q
T
F
F
F
Disjunction (Or):
Disjunction, or "or" (represented by ∨), combines two logical formulas and is true if
at least one of the formulas is true
...
Truth Table:
P
T
T
F
F
Q
T
F
T
F
PvQ
T
T
T
F
Truth Tables:
Truth tables are used to determine when a formula is true or false by listing all
possible combinations of values for the logical variables
...
The truth table for "P and Q" shows it's only true when both P and Q
are true, while "P or Q" is true in three out of the four combinations
...
"P
exclusive or Q" is true when the robot is either blue or has an antenna, but not
when it is neither or both
...
It
states that if P is true, then Q must also be true
...
For example, "If the robot is blue, then it has an antenna" is
only false if there's a blue robot without an antenna
...
For example, "P implies Q" is logically
equivalent to "not P or Q"
...
Conditional Statement:
a conditional statement (also called an implication) is a logical statement of the
form
...
It means that P
implies Q and Q implies P, indicating that P and Q have the same truth value
...
Truth Table :
P
T
T
F
F
Q
T
F
T
F
P↔Q
T
F
F
T
Title: propositional logic gates
Description: Propositional logic uses statements (propositions) that are either true or false. Logic gates are physical or virtual devices that implement Boolean functions—the same kind of logic that propositional logic uses. So, propositional logic gates are electronic representations of logical operations (such as AND, OR, NOT) on propositions.
Description: Propositional logic uses statements (propositions) that are either true or false. Logic gates are physical or virtual devices that implement Boolean functions—the same kind of logic that propositional logic uses. So, propositional logic gates are electronic representations of logical operations (such as AND, OR, NOT) on propositions.