Homework Answers
7 a.
The Boolean Theorm (X+Y)(X'+Y) = Y
This is proved with the veenn diagram
b. X(X'+Y) = XY is explained in the venn diagram
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3. Using Venn Diagrams, prove the following (HINT: Use different colored pen/different patterns of shading to...
5. If possible, draw Venn Diagrams illustrating the following conditions: (a) (A B) = (Cr) B),...
5. If possible, draw Venn Diagrams illustrating the following conditions: (a) (A B) = (Cr) B), and A C. (b) (A u B) (C u B), and A = C. 6.-7. Prove or disprove using Truth Tables that 8. Let X = { a, b, c }, Ys { 2, 3 }. List the elements of (a) Y x X (b) Yx Xx Y 9-12. Given the following formula, shade in the area of the Venn diagram that it represents....
Can anyone help me prove the theorem 49 by using the following hint( Circle)? Here is...
Can anyone help me prove the theorem 49 by using the following
hint( Circle)?
Here is Theorem 39, can't use like right angles are 90 degrees,
or that triangles are 180 degrees.
Strong Right Angle Theorem 49. All right angles are congruer Consequently, a right angle is congruent to another angle if and only if the other angle is also a right angle.) Since you have already proven Theorem 39, it remains only to prove the converse: i f LX...
please help me solve these. discrete structures for computing. Answer the following 1) 2points Use a...
please help me solve these. discrete structures for
computing.
Answer the following 1) 2points Use a table to express the values of the Boolean function: F(x, y, z) = xy + (xyz) 0 0 0 0 0 1 0 1 0 011 1 0 0 1 0 1 110 11 2) 2points) Find the sum-of-products expansion of the Boolean function: F(x, y, z) = (x + 2)y. i.e. 3) (2 points] Express the Boolean function F(x, y, z) = xy...
Solve the following using the Method of Frobenius (y -2n-oanx+') Hint: Use the fact that e-x-1-X+...
Solve the following using the Method of Frobenius (y -2n-oanx+') Hint: Use the fact that e-x-1-X++X 3! 2. xy" + (1-x)y'-y-0
Solve the following using the Method of Frobenius (y -2n-oanx+') Hint: Use the fact that e-x-1-X++X 3! 2. xy" + (1-x)y'-y-0
1 Expectation, Co-variance and Independence [25pts] Suppose X, Y and Z are three different random variables....
1 Expectation, Co-variance and Independence [25pts] Suppose X, Y and Z are three different random variables. Let X obeys Bernouli Distribution. The probability disbribution function is 0.5 x=1 0.5 x=-1 Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y are independent. Meanwhile, let Z = XY. N(0,1). X and Y (a) What is the Expectation (mean value) of X? 3pts (b) Are Y and Z independent? (Just clarify, do not need to prove) [2pts c)...
3) (10 points} Complete the following parts of the problem: a. {5 pts} Implement the function...
3) (10 points} Complete the following parts of the problem: a. {5 pts} Implement the function using CMOS transistors: Z=(WY')+(XY) b. (2.5 pts} If your CMOS circuit is duplicated and connected as follows, complete the timing diagram below {2.5 pts} Reading your timing diagram, what is this circuit? C. W x Z. W 2 X Y 22 Y X Z2
Use Boolean Algebra to simplify the following Boolean expressions to three (3) literals. Please write down...
Use Boolean Algebra to simplify the following Boolean expressions to three (3) literals. Please write down the intermediate steps. 1). F11(x,y,z) = x'yz+xyz +x'y'Z+xy'Z+ xy'z 2). F12(x,y,z) = (y'+xyz')' Question 2 [2 points) Obtain the function expression of F2 from the logic diagram. Question 3 [3 points) Obtain the truth table of the following function and rewrite the function in Canonical POS (Product of Maxterms) format: F3(a,b,c) = (a'+c)(a+b+c') +a'bc' Question 4 (2 points) Convert the following function to Canonical...
2,6,7 help Points: 3 225 23320 Score: (3 pts. (2 pts.] 2 pts. 1. Copy Theorem...
2,6,7 help
Points: 3 225 23320 Score: (3 pts. (2 pts.] 2 pts. 1. Copy Theorem 17.8 and its proof from your textbook (see pages 93-94). Attempt to understand how all parts of the proof come together. C h rial Formula 2. A coin is tossed twelve times. How many sequences with 6 heads and 6 tails are possible? 3. (Page 89, Exercise 16.9) You wish to make a necklace with 20 different beads. In how many different ways can...
can you please prove the following theorem using the provided axioms and defintions. using terms like...
can you please prove the following theorem using the provided
axioms and defintions. using terms like suppose in a paragraph
format. please write clearly or type if you can !
1 Order Properties Undefined Terms: The word "point and the expression "the point z precedes the point y will not be defined. This undefined expression wil be written z < y. Its negation, "z does not precede y," will be written y. There is a set of all points, called...
Please prove the following theorems using the provided axioms and definitions, using terms like s...
Please prove the following
theorems using the provided axioms and definitions, using terms
like suppose, let..ect. Please WRITE CLEARLY AND TYPE IF YOU
CAN.
1 Order Properties Undefined Terms: The word "point" and the expression "the point x precedes the point y" will not be defined. This undefined expression will be written x 〈 y. Its negation, "x does not precede y," will be written X y. There is a set of all points, called the universal set, which is...
5. If possible, draw Venn Diagrams illustrating the following conditions: (a) (A B) = (Cr) B), and A C. (b) (A u B) (C u B), and A = C. 6.-7. Prove or disprove using Truth Tables that 8. Let X = { a, b, c }, Ys { 2, 3 }. List the elements of (a) Y x X (b) Yx Xx Y 9-12. Given the following formula, shade in the area of the Venn diagram that it represents....
Can anyone help me prove the theorem 49 by using the following
hint( Circle)?
Here is Theorem 39, can't use like right angles are 90 degrees,
or that triangles are 180 degrees.
Strong Right Angle Theorem 49. All right angles are congruer Consequently, a right angle is congruent to another angle if and only if the other angle is also a right angle.) Since you have already proven Theorem 39, it remains only to prove the converse: i f LX...
please help me solve these. discrete structures for
computing.
Answer the following 1) 2points Use a table to express the values of the Boolean function: F(x, y, z) = xy + (xyz) 0 0 0 0 0 1 0 1 0 011 1 0 0 1 0 1 110 11 2) 2points) Find the sum-of-products expansion of the Boolean function: F(x, y, z) = (x + 2)y. i.e. 3) (2 points] Express the Boolean function F(x, y, z) = xy...
Solve the following using the Method of Frobenius (y -2n-oanx+') Hint: Use the fact that e-x-1-X++X 3! 2. xy" + (1-x)y'-y-0
Solve the following using the Method of Frobenius (y -2n-oanx+') Hint: Use the fact that e-x-1-X++X 3! 2. xy" + (1-x)y'-y-0
1 Expectation, Co-variance and Independence [25pts] Suppose X, Y and Z are three different random variables. Let X obeys Bernouli Distribution. The probability disbribution function is 0.5 x=1 0.5 x=-1 Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y are independent. Meanwhile, let Z = XY. N(0,1). X and Y (a) What is the Expectation (mean value) of X? 3pts (b) Are Y and Z independent? (Just clarify, do not need to prove) [2pts c)...
3) (10 points} Complete the following parts of the problem: a. {5 pts} Implement the function using CMOS transistors: Z=(WY')+(XY) b. (2.5 pts} If your CMOS circuit is duplicated and connected as follows, complete the timing diagram below {2.5 pts} Reading your timing diagram, what is this circuit? C. W x Z. W 2 X Y 22 Y X Z2
Use Boolean Algebra to simplify the following Boolean expressions to three (3) literals. Please write down the intermediate steps. 1). F11(x,y,z) = x'yz+xyz +x'y'Z+xy'Z+ xy'z 2). F12(x,y,z) = (y'+xyz')' Question 2 [2 points) Obtain the function expression of F2 from the logic diagram. Question 3 [3 points) Obtain the truth table of the following function and rewrite the function in Canonical POS (Product of Maxterms) format: F3(a,b,c) = (a'+c)(a+b+c') +a'bc' Question 4 (2 points) Convert the following function to Canonical...
2,6,7 help
Points: 3 225 23320 Score: (3 pts. (2 pts.] 2 pts. 1. Copy Theorem 17.8 and its proof from your textbook (see pages 93-94). Attempt to understand how all parts of the proof come together. C h rial Formula 2. A coin is tossed twelve times. How many sequences with 6 heads and 6 tails are possible? 3. (Page 89, Exercise 16.9) You wish to make a necklace with 20 different beads. In how many different ways can...
can you please prove the following theorem using the provided
axioms and defintions. using terms like suppose in a paragraph
format. please write clearly or type if you can !
1 Order Properties Undefined Terms: The word "point and the expression "the point z precedes the point y will not be defined. This undefined expression wil be written z < y. Its negation, "z does not precede y," will be written y. There is a set of all points, called...
Please prove the following
theorems using the provided axioms and definitions, using terms
like suppose, let..ect. Please WRITE CLEARLY AND TYPE IF YOU
CAN.
1 Order Properties Undefined Terms: The word "point" and the expression "the point x precedes the point y" will not be defined. This undefined expression will be written x 〈 y. Its negation, "x does not precede y," will be written X y. There is a set of all points, called the universal set, which is...
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