# Tagged Questions

42 views

### Finding the contrapositive of the statement “I go to school if it does not rain”

I got this question in a exam.There were two more statements in the examination(but they were quite clearly wrong).However I got stuck between these two statements.The contrapositive of the the ...
46 views

### Do brackets around negation signify negating the input or output - Boolean Algebra Logic Circuits

I know that $\overline{p + q}$ will result in the input to the logic gate being p, and q, and we can negate this by using an or gate, followed by a not gate, or we can just use a nor gate. However, ...
25 views

### Dont understand application of Demorgans Law when simplifying to Sum of Products Form - Boolean Algebra

I'm having trouble trying to understand how this can be simplified. I'm stuck at the first part... The expression is: where a AND b is ab or a*b, and ...
50 views

98 views

### Boolean Algebra simplify minterms

I have this equation $$\bar{A}\cdot\bar{B}\cdot\bar{C} + A\cdot\bar{B}\cdot C + A\cdot B\cdot \bar{C} + A \cdot B\cdot C$$ and need to simplify it. I have got as far as I can and spent a good 2 ...
68 views

### simplify boolean algebra expressions

Use Boolean algebra to simplify the expression for F1, where, F1 = A’.B’.C’.D’ + A’.B’.C.D’ + A’.B’.C.D + A’.B.C’.D + A’.B.C.D’ + F2 and F2 = A’.B.C.D + A.B’.C’.D’ + ...
85 views

### How to prove this equality using boolean algebra?

I have approximately no idea on how to solve the following problem, so any help would very much be appreciated: $$x' y'+ x y = (x y' + x' y)'$$ I can't figure out how to prove the equalities ...
125 views

### Find the disjunctive normal form and then simplify

Let $f(x,y,z,w)=zw+z'w'+xy'z'w+xyz'w$ Disjunctive normal form $zw(x'+x)(y'+y)+z'w'(x'+x)(y'+y)+xy'z'w+xyz'w=(zwx'+zwx)(y'+y)+(z'w'x'+z'w'x)(y+y')+xy'z'w+xyz'w$ ...
742 views

### Is it logically valid to prove DeMorgan's laws using the duality of boolean algebra?

I'm taking an introductory course in boolean algebra, and have been assigned the task of proving DeMorgan's Laws (so, disclaimer, this is homework). One line of reasoning that I came up with would be ...
339 views

### Boolean formula over 64 Boolean variables X

This question comes from this homework assignment from ECS20 at UC Davis. Chess is played on an 8 x 8 board. A knight placed on one square can move to any unoccupied square that is at a distance ...
324 views

### Disjunctive normal form expansion

I do not understand this at all. Find the sum-of-products expansions of these Boolean functions. $F(x, y, z) = x + y + z$ $F(x, y, z) = (x + z)y$ $F(x, y, z) = x$ $F(x, y, z) = x y$ ...
123 views

### Boolean algebra simplification

I have the equation (CD)+(BC'D'+A'B'C'D)+(C'D') and I can't seem to simplify it enough for my homework. I've tried multiple ways of simplifying the equation and I keep ending with an extra variable D. ...
67 views

36 views

### Question about poset and boolean ordering, inf and sup

We have a poset $(X, \sqsubseteq)$, and we define operations $+$ and $\cdot$ by $x+y=inf(x, y)$ and $x\cdot y=sup(x, y)$ ($+$ can be seen as union in sets and $\cdot$ as intersection in sets). The ...
147 views

### Solving Boolean Expressions with Theorems

I'm having the hardest time wrapping my head around this stuff. This is a homework problem, one of many. I just need some help on what to do. ...
59 views

In $A=\{2, 3, 6, 12, 36, 72, 108\}$ we define the relation $R$ by $aRb$ if $b=a$, or $b=2a$ or $b=3a$. Q1: Draw the graph of $R$ and list which properties $R$ has. A1: The properties are: ...
69 views

### How to prove boolean ordering question

Let $\sqsubseteq$ be the boolean ordering of $X$, so for every $x$ and $y$ applies $x \sqsubseteq y$ if $x \sqcap y = x$. Let $v, w, a, b \in X$ with $v \sqsubseteq a$ and $w \sqsubseteq b$. Show that ...
46 views

### How do I solve this Boolean Algebra Problem?

Let A be an arbitrary but fixed Boolean algebra with operator $@$ and $*$ and $'$ and the zero and unit element be denoted by $0$ and $1$ respectively. let $x,y,z \in A$ if $a,y \in A$ such that ...
39 views

### Need help for right direction simplifying boolean algebra formula

I have the following boolean algebra, where union is $+$ and intersection is $\cdot$ : $(x\cdot y)+((z+y)\cdot \bar{z})+y=y$ Is there a systematic way of doing this, or do you need to puzzle? My ...
46 views

### Help with getting the right direction on a boolean algebra question

Need some help getting in the right direction for answering the following question: Prove the following property and interpret this in $\mathcal P \left ({V} \right)$: if $x+ \bar y=$ 1, then ...
88 views

### How are boolean expressions converted to NOR expressions?

What kind of rules help to convert an expression into a 3 input NOR expression? Do all variables have to be of the form (a+b+c)' + (d+e+f)'? What happens if there is an expression that is just (a')' ...
57 views

### Modify boolean equation to get 3 input NOR equation using boolean algebra rules

I was taking a look at this link http://lizarum.com/assignments/boolean_algebra/chapter3.html to try and solve an equation I have. The original equation is: H = MC + MC' + CRD + M'CD' I simplified ...
78 views

### Multiply the number $(1001)_{2}$ by 3 digit number

I want to multiply the number $(9)_{10} \rightarrow (1001)_{2}$ by a 3 digit binary number. 1) How I can extract the boolean equations? 2) Make a circuit of it. so what I did is just see what ...