Problem solving using truth tablePresentation Transcript
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TRUTH TABLE AND PROBLEM SOLVING email@example.com @Vishnu_Kishor
BOOLEAN ALGEBRA• Boolean algebra (or Boolean logic) is a logical calculus of truth values• It’s algebra of two values.• These are usually taken to be 0 and 1• Also F and T, false and true, etc. are also in common use.
TRUTH TABLE• A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions etc• Used to compute the functional values of logical expressions on each of their functional arguments
• Each row of the truth table therefore contains one possible configuration of the input variables and the result of the operation for those values
LOGIC GATES• A logic gate is an idealized or physical device used for implementing a Boolean function• It performs a logical operation on one or more logic inputs and produces a single logic output• Logic gates are primarily implemented using diodes or transistors acting as electronic switches• can also be constructed using electromagnetic relays, fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements.
Use a truth table to test the validity of the following argument.
Q1) If you invest in the VK Corporation, thenyou get rich.You didnt invest in the VK Corporation.Therefore, you didnt get rich.A. ValidB. Invalid
• Step 1-Symbolize the argument. Let p be the statement "You invest in the VK Corporation." Let q be the statement "You get rich."Then the argument has this symbolic form:• Step 2-Make a truth table having a column for each premise and for the conclusion
• Step 3-Interpret the truth table. Notice that in the third row, the conclusion is FALSE while both premises are TRUE. This tells us that the argument is INVALID.
Q2) If you are a hound dog, then you howl atthe moon.You dont howl at the moon.Therefore, you arent a hound dog.A. ValidB. Invalid
• Step 1-Symbolize the argument.Let p be the statement "You are a hound dog." Let q be the statement "You howl at the moon.“.Then the argument has this symbolic form:• Step 2-Make a truth table having a column for each premise and for the conclusion.
• Step 3-Interpret the truth table. Notice that in this truth table, there is NO ROW in which conclusion is FALSE while both premises are TRUE. This tells us that the argument is VALID.
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