(Fuzzy logic.) In fuzzy logic, a proposition (a claim that something is true) has, instead of a binary truth value (0 or 1), a real-valued truth value in the interval [0, 1]. Researchers are modelling a particular proposition's truth value with the random variable X that has density f(x) = [cx (1-x), 10, 0 ≤ x ≤ 1, otherwise. (a) Determine the constant c. The density must integrate to 1. (b) Determine the cumulative distribution function of X, and draw it. (c) Calculate the probability that the truth value is at least 0.75. (d) Find the mode of the distribution, that is, the point x where the density f(x) attains its maximum.

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Q: (20 pts) Use the rules of inference to show that if Vx(A(x) → B(x)), 3x(B(x) v C(x)) and Vx¬(D(x)…

A: To prove that if , , and are true, then is also true, you can use rules of inference, specifically…

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A: Hello there! there are more than three subparts in the question. According to our policies we cannot…

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Q: Q #x (P(x) V (P(x)) x (7Q(x) V √(x)) # 18 76c

A: This is a question of Predicate Logic.

Q: #3

A: We are going to use the formula

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Q: 13 (Gv H), (GVU) + U 1 (Gv H) :PR (GVU) 2 :PR

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A: So,we take the inversion of x  and  z. Product that we will get x¯z=1111000001010101=01010000

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