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
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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.
Transcribed Image Text: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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