The image contains mathematical text related to Boolean algebra, specifically on the topic of representing functions in terms of minterms and maxterms.---**Equations:**1. **Equation (5.3.2):** \[ F(x, y, z) = (x + y' + z')(x + y + z')(x' + y + z')(x' + y' + z) = M_2 \cdot M_3 \cdot M_4 \cdot M_7 = \prod(2, 3, 4, 7) \] This equation expresses the function in product of maxterms form, where each term in the product is a sum of literals. The notation \(\prod(2, 3, 4, 7)\) indicates the maxterms corresponding to binary indices 2, 3, 4, and 7.2. **Equation (5.3.1):** \[ F(x, y, z) = x' y' z' + x' y z' + x y' z' + x y z' = m_0 + m_1 + m_5 + m_6 = \sum(0, 1, 5, 6) \] This equation shows the function expressed as a sum of minterms, where each term in the sum is a product of literals. The notation \(\sum(0, 1, 5, 6)\) represents the minterms corresponding to binary indices 0, 1, 5, and 6.---Both equations illustrate that summing minterms and taking products of maxterms in Boolean expressions are complementary approaches for describing the same functionality.

unctionality. This shows that the sum of minterms and product of maxterms re complementary. F(x, y, z) = (x + y + 2) - (z+y+2)-(z'+y+z). (z' + y + 2) = M₂ M3 M4 M₂ = - II(2,3,4,7) F(x, y, z)=z' y. 2+2·y.z+zy.z+z. y. 2 =mo+m₁ +ms + me = - Σ(0,1,5,6) (5.3.2) in-context (5.3.1) in-context

unctionality. This shows that the sum of minterms and product of maxterms re complementary. F(x, y, z) = (x + y + 2) - (z+y+2)-(z'+y+z). (z' + y + 2) = M₂ M3 M4 M₂ = - II(2,3,4,7) F(x, y, z)=z' y. 2+2·y.z+zy.z+z. y. 2 =mo+m₁ +ms + me = - Σ(0,1,5,6) (5.3.2) in-context (5.3.1) in-context

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

The image contains mathematical text related to Boolean algebra, specifically on the topic of representing functions in terms of minterms and maxterms.

---

**Equations:**

1. **Equation (5.3.2):**
\[
F(x, y, z) = (x + y' + z')(x + y + z')(x' + y + z')(x' + y' + z)
= M_2 \cdot M_3 \cdot M_4 \cdot M_7
= \prod(2, 3, 4, 7)
\]

This equation expresses the function in product of maxterms form, where each term in the product is a sum of literals. The notation \(\prod(2, 3, 4, 7)\) indicates the maxterms corresponding to binary indices 2, 3, 4, and 7.

2. **Equation (5.3.1):**
\[
F(x, y, z) = x' y' z' + x' y z' + x y' z' + x y z'
= m_0 + m_1 + m_5 + m_6
= \sum(0, 1, 5, 6)
\]

This equation shows the function expressed as a sum of minterms, where each term in the sum is a product of literals. The notation \(\sum(0, 1, 5, 6)\) represents the minterms corresponding to binary indices 0, 1, 5, and 6.

---

Both equations illustrate that summing minterms and taking products of maxterms in Boolean expressions are complementary approaches for describing the same functionality.

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