A Class-Room Introduction to Logic

May 4, 2009

Unit-XV: Truth-functional Logic

Filed under: Logic,Truth Table Method — Dr. Desh Raj Sirswal @ 6:25 am

Truth table: An array on which all possible truth values of compound statements are displayed, through the display of all possible combinations of the truth values of their simple components. A truth table may be used to define truth-functional connectives; it may also be used to test the validity of many deductive arguments. To draw truth table follow this formula:

Number of rows = 2n

2 represents constant for truth and falsity.

n represents “number of discrete atomic components.”

Its means also then how many component in the given compound statement. In the below example there is only two component p and q so we draw truth table like this. 2 x 2 =4, in first column  we add two Ts and two Fs and second we add one T and one F and so on. If there is 3 component we draw 8 rows. Two number of rows increase with the number of component.

For example: p≡q (If and only if Ram will pass BA, then he will join MA.)

p q p≡q
T T T
T F F
F T F
F F T

Truth Value: The status of any statement as true, or false.

Truth-Functional Component: Any component of a compound statement whose replacement by another statement  having the same truth value would not change the truth value of the compound statement.

Truth-Functional Connective: Any logical connective (including conjunction, disjunction, material implication, and material equivalence) between the components of a truth –functional compound statement.

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