Discrete Math Problems: Boolean Algebra
Not what you're looking for?
1. Let x, y be elements in the Boolean algebra B. Prove that x = y if and only if xy + xy = 0.
2. a. How many rows are needed to construct the (function) table for a Boolean function of n variables?
b. How many different Boolean functions of n variables are there?
3. Let g: B4 →B be defined by g(w, x, y, z) = (wz + xyz)(x + x yz).
a. Find the d.n.f. and c.n.f. for g.
b. Write g as a sum of minterms an d as a product of maxterms (utilizing binary labels).
4. Obtain a minimal-product-of-sums representation for f (w, x, y, z) IIM(0, 1, 2, 4, 5, 10, 12, 13, 14).
5. Let f, g: B5 →B be Boolean functions, where f =∑m(1, 2, 4, 7, x) and g = ∑m(0, 1, 2, 3, y, z, 16, 25). If f ≤ g, what are x, y, z?
Purchase this Solution
Solution Summary
Discrete mathematics for Boolean algebra are discussed. How many rows are needed to construct the function tables for a Boolean function of n variables is provided.
Solution Preview
Please see attachment for detailed solution.
1. Let x, y be elements in the Boolean algebra B. Prove that x = y if and only if xy + xy = 0.
If x=y, then xy+ xy = x2+x2= x+x=0
If xy + xy = 0, then xy = 0 and then x=y = 0.
2. a. How many rows are needed to construct the (function) table for a Boolean function of n variables?
There are Boolean functions.
b. How many different Boolean functions of n variables are there?
There are different Boolean functions.
3. Let g: B4 →B be defined by g(w, x, y, z) = (wz ...
Education
- BSc, University of Bucharest
- MSc, Ovidius
- MSc, Stony Brook
- PhD (IP), Stony Brook
Recent Feedback
- "Thank you "
- "Thank You Chris this draft really helped me understand correlation."
- "Thanks for the prompt return. Going into the last meeting tonight before submission. "
- "Thank you for your promptness and great work. This will serve as a great guideline to assist with the completion of our project."
- "Thanks for the product. It is an excellent guideline for the group. "
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.