what type of method is shorter truth table
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Answer:
You can think of the shortened truth table technique as like a game with permitted and forbidden moves. The objective of the game is to find a row out of all the rows in a full truth table which has all true premisses and a false conclusion. Such a row, if it exists, would, of course, show the argument to be invalid.
Mathematics normally uses a two-valued logic: every statement is either true or false. You use truth tables to determine how the truth or falsity of a complicated statement depends on the truth or falsity of its components.
Complex, compound statements can be composed of simple statements linked together with logical connectives (also known as "logical operators") similarly to how algebraic operators like addition and subtraction are used in combination with numbers and variables in algebra. Conjunction (AND), disjunction (OR), negation (NOT), implication (IF...THEN), and biconditionals (IF AND ONLY IF), are all different types of connectives.
Independent, simple components of a logical statement are represented by either lowercase or capital letter variables. These variables are "independent" in that each variable can be either true or false independently of the others, and a truth table is a chart of all of the possibilities. Therefore, if there are NN variables in a logical statement, there need to be 2^N2
N
rows in the truth table in order to list out all combinations of each variable being either true (T) or false (F). For example, if there are three variables, A, B, and C, then the truth table with have 8 rows:
P Q R
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F