38.a,b,c,d CHAPTER 1 Formal Logic 38. Propositional wffs and truth tables belong
ID: 3143665 • Letter: 3
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38.a,b,c,d
CHAPTER 1 Formal Logic 38. Propositional wffs and truth tables belong to a system of two-valued logic because every 1. In fuzzy logic, or thing has one of two values, F or T, which we can think of as 0 or many-valued logic, statement letters are assigned values in a range between 0 and 1 to reflect some "probability" to which they are false or true. A statement letter with a truth value of 0.9 is "mostly true" or "has a high probability of being true" while a statement letter with a truth value of 0.05 "has a very high probability of being false." Fuzzy logic is used to manage decisions in many imprecise situations such as robotics, manufacturing, or instrument control. Truth values for compound statements are determined as follows: A' has the truth value 1- A. A A B has the truth value that is the minimum of the values of A and of B. A V B has the truth value that is the maximum of the values of A and of B. a. Explain why these are reasonable assignments for the truth values of A',A A B, and Suppose the statement "Flight 237 is on time" is estimated to have a truth value of 0.84, and the statement "Runway conditions are icy" is estimated to have a truth value of 0.12 Find the truth values of the following statements: b. Runway conditions are not icy * c. Runway conditions are icy and Flight 237 is on time. d. Runway conditions are icy or Flight 237 is not on time. Four machines, A, B, C, and D, are connected on a computer network. It is feared that a computer virus may have infected the network. Your security team makes the following statements: 1. If D is infected, then so is C 2. If C is infected, then so is A.Explanation / Answer
A): A TRUTH-VALUE table consists of a truth-value (either true or false) of an assignment to each sentence of sentential logic, not just those atomic formulae that appear in some particular formula. We can determine truth value of any sentence relative to given truth value asignment.
A' - > 1 - A (This means that if A has value 0.6 then value of A' will be 0.4. This defines that if the possibility of A being true is 0.6 then Possiblity of A being false is 0.4)
A / B (This means A and B that is Together possibilty of A and B true or False)
A / B (This means A or B that is possibilty of A or Possibility B being either true or False)
B): Runway Conditions are icy True = 0.84
A' - > 1 - A
Runway Conditions are not icy True = 1 - 0.12 = 0.88
C): Runway Conditions are icy and Flight is on time = 0.84*0.12 = 0.1008
If A , B are independent then P(A/B) = P(A) *P(B)
D): Runway Conditions are icy and Flight is not on time = 0.16+0.12 = 0.28
If A,B are mutually exclusive events, then P(A or B)= P(A) + P(B)
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