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Logic of Compound Statements

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A statement consists of one or more sub statements named as compound statement and these sub statements are connected by one or more logical connectives. As the name suggests a compound statement refers the statement form.
A statement could have two cases either it could have true or false but both could not occur together. The logic of compound statements can be calculated but be sure about the sub statements as they could be either true or false.

  • A compound statement that is always true does not depend upon the truth value of sub - statements named as tautology.
  • A compound statement that is always false does not depend upon the truth value of sub - statements named as contradiction.
  • A compound statement that is neither true nor false means neither tautology or contradicted is named as contingent statement.
Mathematical logic deals with the formal reasoning. A compound statement is also named as block and appears as the body of another statement. Declarations came in the starting of the statement which explains the compound statement from the declaration Point to the end of the block. In a compound statement identifiers are reputed auto till the declaration. Register, static and extern are some classes of compound statements and Functions can only be extern.
If a variable is declared in a compound statement with storage class extern then the initialization would not be permitted. If a variable is declared with the auto or register keyboards then they are reallocated and if needed then each time they are initialized with the entrance of compound statement.
In short a compound statement has the sub statements that are enclosed in curly braces and sometimes named as blocks also. A compound statement can be used at any place where a statement is probable.

Symbolic Logic

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In mathematics, symbolic logic is a method which is used to characterize logical expressions using symbols and variables, relatively than in ordinary language.
It is used in removing the uncertainty which normally accompanies in ordinary languages, such as English, and allows easier operation.
In mathematics, there are so many systems of symbolic logic which are shown below:
1. Classical propositional logic,
2. First-order logic,
3. Modal logic.
All symbolic logic is divided by different symbols, or eliminates the use of certain symbols.
Now, we will see the symbolic logic symbols table. Now we will see the basic logic symbols which are mention below:
1. (┑): - This symbol is named as negation.
Explanation: Suppose we have a statement ┑S which is true if and only if the value of S is false.
= ┑ (┑S) ⇔ S
2. (∨): - This symbol is named as logical disjunction.
Explanation: The statement S ∨ T is true if the value of S and T both are true, or if both are false.
3. (⊕): - This symbol is named as exclusive disjunction.
Explanation: Suppose we have a given statement S ⊕ T then given condition is true when value of S and T are true but not both the value true.
4. (T): - This symbol is named as Tautology.
Explanation: Meaning of this symbol is S ⇒⊤ is always true.
1. (∃): - This symbol is named as existential quantification.
Explanation: Suppose we have a given statement ∃ x S (x), it means there is at least one x such that S(x) is true.
1. (∃!): - This symbol is named as uniqueness quantification.
Explanation: Suppose we have a given statement ∃! x S (x), it means there is exactly one x such that S(x) is true.
This is all about symbol logic.