Let P(x) denote “x + 2 ≥ 5 ”, find the truth values for the following compound propositions:
a. P(1) ∨ P(-2)
b. P(4) ∧ P(3)
c. P(2) ∨ p(x)
i am done perfectly
Anything doubtful or not understand just comment I will touch with you
Please thumsup for my effort
Thank you and all the best
Let P(x) denote “x + 2 ≥ 5 ”, find the truth values for the following...
Please answer question 1 and 2. (1) Let p, q be propositions. Construct the truth table for the following proposition: (2) Let X be the set of all students in QC and let Y be the set of all classes in the Math Department available for QC students in the Fall 2019. Leyt P(z, y) be the proposition of the course y. Write down the following propositions using quantifiers: e Some QC students read the description of each course in...
2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd x< 3 If the universe consists of all integers, circle which of the following are TRUE and cr oss out the ones that are FALSE: q(1) p(7) V q(7) P(3) -(p(-4) V q3)) P(3) A q(4) 3ax [p(r) A q(x) p4) A3) (г)Ь ТА 2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd x
QUESTION 18 Let M and m denote the maximum and the minimum values of f(x, y) = x2 - 2x + y2 +3 in the disk 2? + y2 < 1. Find M + m. OA 8 OB. 7 Ос 5 OD 4 OE 12
marks] Let P(x) denote the statement that rs8 (where r is an integer). What is the truth value of: a) P(2)
Let ??~N(3, 9) and ?? = 5 ? ??. a) Find P(X > 2) b) Find P(?1 < Y < 3) c) Find P(X > 4|Y < 2) Please use an approximation to calculate the value of ?(x), where necessary
UIC 5. (20 pt.) Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (5 pt.) (p^ q) → (q V r) b. (5 pt) P)Ag)- Vg)A(A-r)- c. (10 pt.) Additional Topics: Satisfiability (10 pt.) A compound proposition is said to be satisfiable if there is an assignment of truth values to its variables that makes it true. For example. p ^ q is true when p = T and q = T;thus, pAqissatsfiable....
Let descrete random variable X - Bin(9,0.3) Find: 1) Probability P(X>5) 2) Probability P( X 2 ) 3) Probability P(2<x<5) 4) Probability P(2<x<5) 5) Probability P(X=0) 6) Probability P(X= 7) 7 Mx 8) Ox Show your explanations. Displaying only the final answer is not enough to get credit Note: round calculated numerical values to the fourth decimal place where applicable.
A lab has six computers. Let X denote the number of those computers that are in use at a particular time of day. Suppose that the probability distribution of X is given in the following table 0 f(x) = P(X=x) 0.05 F(x) = P(XSX) 1 0.1 2 0.15 3 0.25 14 10.2 0.2 S6 5 K 0.1 1. Find k. 2. Find the probability that at least 3 computers are in use. 3. Find the probability that between 2 and...
QUESTION 2 a. Let p and q be the statements. i Construct the truth table for (-p V q) ^ q and (-p) v q. What do you notice about the truth tables? Based on this result, a creative student concludes that you can always interchange V and A without changing the truth table. Is the student, right? ii. Construct the truth tables for (-p VG) A p and (-p) v p. What do you think of the rule formulated...
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.