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Discrete Mathematics: Boolean Products

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2. For the zero-one matrix
| 1 0 0 |
B= | 0 1 1 |
| 1 0 1 |

A) Find B[2] = B ○ B and B[3] = B ○ B[2]

B) Use a) and induction to fine B[n] = B ○ B ○...○B (n times)

********* Please note the ○ sign represent Boolean operator, there should be a dot the middle of this circle but I couldn't find the symbol to enter it in my text so I used this instead. thanks***********

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Boolean products are investigated.

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Discrete Math Problems: Boolean Algebra

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?

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