by sheila_blige

Introduction to symbolic logic truth tables:

Logic contracts with kinds of reasoning. Reasoning may be legal opinion or mathematical confirmations. Basic logical connectives are AND, OR and NOT. Symbolic form of logical connectives are’^^’, ‘vv’ and ‘~’ for AND, OR and NOT respectively. Truth table states the relation between the compound statement and sub – statement. Let us see symbolic logic truth tables in this article.

Symbolic Logic Truth Tables:

Logic:

Logic contracts with kinds of reasoning. Reasoning may be legal opinion or mathematical confirmations.

Logical statement:

Logical statement is a sentence which is any one true or false but not mutually.

Example:

Statement 1: Delhi is capital of India.

Statement 2: twenty divide by five is 6.

Statement 3: what is your name?

Here

Statement 1 is true and it is also a statement.

Statement 2 is false but it is a statement.

Statement 3 is cannot be assigned to true or false and it is also a question not a statements.

Basic logical connectives:

And or conjunction

Or / disjunction

Not or negation.

Symbols to represent logical connectives:

‘^^’ = AND

‘vv’ = OR

~ = NOT

Truth table:

A table that explains the connection between the truth values of a compound statement and truth values of its sub- statements is described the truth table.

Truth table holds of rows and columns.

The first column is filled with possible truth values of the sub – statement and final column is filled with truth values of the compound statement on the foundation of truth values of the secondary – statement written in the initial columns.

2n rows are presence in the truth table.

If the statement is true, we say that is truth value is true or T and if the statement is false, we say that is truth value is false or F

Symbolic truth table for logical connectives:

Conjunction or AND:

A B A’^^’ B

T T T

T F F

F T F

F F F

Disjunction / OR:

A B A’vv’ B

T T T

T F T

F T T

F F F

Negation or NOT:

A ~A

T F

F T

Problems for Symbolic Logic Truth Tables:

Problem 1:

Solve A’^^'(~A)

Solution:

Given

A ‘^^'(~A)

A ~A A ‘^^'(~A)

T F F

F T F

Problem 2:

Solve (~A)’vv’ (~B)

Solution:

Given

(~A)’vv’ (~B)

A B ~A ~B (~A)’vv'(~B)

T T F F F

T F F T T

F T T F T

F F T T T

**Logic**

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*Logic*

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