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# Discrete Math Problems: Boolean Algebra

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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?

https://brainmass.com/math/discrete-math/discrete-math-problems-boolean-algebra-561669

#### 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 ...

#### 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.

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## Discrete math questions on relations and functions

Logic & Set Theory; Boolean Algebra; Relations & Functions

1. How do we distinguish relations from functions?

2. What sort of relation is friendship, using the human or sociological meaning of the word? Is it necessarily reflexive, symmetric, antisymmetric, or transitive? Explain why it is or is not any of these. What other types of interpersonal relationships share one or more of these properties? Explain.

3. Reduce the following Boolean product to zero OR a fundamental product: xyx'z.c

4. Write the dual of the following Boolean equation: a+a'b = a+b

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