Question: Show that in a Boolean algebra, the idempotent laws x x = x and x x = x hold for every element x.

Show that in a Boolean algebra, the idempotent laws x ∨ x = x and x ∧ x = x hold for every element x.

Step by Step Solution

★★★★★

3.55 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We need to play around with the symbols until the desired resul... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

923-M-C-M-S (2584).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Show that in a Boolean algebra, the complement of the element 0 is the element 1 and vice versa.

Q:

Show that in a Boolean algebra, if x y = 0, then x = 0 and y = 0, and that if x y = 1, then x = 1 and y = 1.

Q:

Let B be a Boolean algebra that is partially ordered by . For all x, y B prove that (a) x y if and only if + y = 1; and (b) x if and only if xy = 0.

Q:

Need help with Boolean algebra. Using these laws how do I show that F and G are equivalent? OR Form Identity Name AND Form Identity Law Null (or Dominance) Law Idempotent Law Inverse Law Commutative...

Q:

(a) Let + and denote addition and multiplication, respectively, and define ' by x' = 1 x, for all x R. Is (R, +, , ', 0, 1) a Boolean algebra? If so, show that properties B1 B5 (attached) hold. If...

Q:

Show that in a Boolean algebra, every element x has a unique complement x such that x v v x = 1 and x ? ? x = 0 .

Q:

Show that in a Boolean algebra, every element x has a unique complement x such that x v v x = 1 and x ? ? x = 0 .

Q:

subject computer architecture and organization section digital logic design QUESTION 2: I (a) Design a combinational circuit with three inputs, A, B, and C, and three outputs, X, Y, and Z. When the...

Q:

The following is an example of which of the laws of Boolean algebra? x + 0 = x x 1 = x Group of answer choices Domination laws Double complement law Identity laws

Q:

For an element x of a Boolean algebra B , the element x ' is called the complement of x and x + x ' = 1 .

Q:

Reginald paid several different types of taxes during the past year. He expects to be able to itemize his deductions. Taxes paid were real property tax $3,100; excise tax on gasoline of $850; sales...

Q:

Access the Web site of the Recording Industry Association of America (www.riaa.com). Discuss what you find there regarding copyright infringement (that is, downloading music files). How do you feel...

Q:

STWA Inc. operates as a sole proprietorship. Now the sole owner has decided to convert the business into a regular corporation. Which of the following should be expected as a result of the change?...

Q:

6. The critical value of a statistic defines the . a. top 2.5% of the distribution for a one-tailed hypothesis b. bottom 2.5% of the distribution for a one-tailed hypothesis c. extreme 5% of the...

Q:

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the -axis. Sketch the region and a typical shell. 9. 1+ ?,...

Q:

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. Sketch the region and a typical shell. 15. y x, y = 0, x...

Q:

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 21. y = In x, y= 0, x= 2: about the y-axis...

Q:

Use the table for the question(s) below. Consider the following probability distribution of returns for Alpha Corporation: The expected return for Alpha Corporation is closest to: 0.00% 10% 6.67%...

Q:

M&M Proposition I with taxes states that the: Select one: a. Value of a levered firm is equal to the present value of the interest tax shield plus the value of an unlevered firm. b. Required return...

Q:

A leader who sets levels of expectation, then gives direction and guidance and determines work schedules uses what type of leadership theory? O A. Supportive O B. Directive OC. Participative O D....