Find propositional logic formulas expressing the following statements:

Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 but not by 7. (b) are divisible by 5. (c) have distinct digits. (d) are divisible by 5 or by 7 (inclusive or).

In semiotics a sign is .

Alice, a friend of Mr. Bernard’s, wants to compose a song. She asks Mr. Bernard for help. Although Mr. Barnard knows nothing about music, he finds that the sequence of notes in a numbered musical notation can be expressed as an FSM with input the alphabet {1, 2, 3, 4, 5, 6, 7} ("do", "re", "mi", "fa", "so", "la", "ti"). b)Alice changes her mind. She finds that it would be enough to just use {1, 5} ("do", "so") in her new song. She wants to compose a song satisfying the following two conditions: i)If the sequence of notes ends with "1", it should contain an even number of digits. ii)If the sequence of notes ends with "5", it should contain an odd number of digits. Please draw an FSM that only accepts the sequences of notes that satisfy the above conditions.Note that you should provide a detailed description of the FSMs in your design to show how it works. Specifically, you should describe the meaning of each state

: Simplify the following Boolean expressions to a minimum * :number of literals F = abc + (a + c) + ābc

The equation XA + XB = XA+B is always held. Group of answer choices True False

(RS + R)* RS = (RR*S)* true or false prove and explain

= =×ばつ2 and 6 = (a) A composite number is a positive integer that has at least one divisor other than 1 and itself. For example, 2 ×ばつ2 is not a composite number but 4 2 ×ばつ 3 are composite numbers. A logic circuit has four binary input variables, A, B, C and D. The output Z of the logic circuit is 1 if the unsigned integer represented by the binary number ABCD is a composite number. Using variables A and B for the select inputs S1 and S0 of a 4-to-1 multiplexer, implement the logic function Z(A, B, C, D) using this multiplexor and other logic gates.

Alice, a friend of Mr. Bernard’s, wants to compose a song. She asks Mr. Bernard for help. Although Mr. Barnard knows nothing about music, he finds that the sequence of notes in a numbered musical notation can be expressed as an FSM with input the alphabet {1, 2, 3, 4, 5, 6, 7} ("do", "re", "mi", "fa", "so", "la", "ti"). Alice wants to compose a song that contains the pattern "15" an even number of times. Please draw an FSM that only accepts a sequence of notes that satisfies the above pattern. Note that you should provide a detailed description of the FSMs in your design to show how it works. Specifically, you should describe the meaning of each state.

Simplify the following expressions by applying Boolean rules. L(LM + M)

Q1- Example 1: Write a program that solves a quadratic equation using Quadratic equation -b± vb2 – 4ac 2a b2 – 4ac> 0 -b b2 – 4ac = 0 2a If the sub-radical value is less than zero, print the expression (the root is complex) Q2:- write matlab code to sum the following x3 + x7

A repeating ground-track orbit has period of repetition is two orbits per day (ω⊕ = 7.2921151467 · 10−5 rad/s), has an eccentricity of 0.74, an inclination of 63.4349 deg, a right ascension of the ascending node of −86.915798 deg, and argument of perigee of 270 deg. What is the semi-major axis? In MATLAB, provide the following results using 100 points equally distributed in time over an orbital period with a starting position of true anomaly equal to 0 degrees: 3D representation of the orbit. Include the Earth (as a simple sphere) in the center of the plot for a size comparison. Make sure that the axis have the same scale.

() Wride the bonlowering in mathematica expression z= Je'ry? + loe-yt b. q EK