Exercise 5.4 in Engineering Mathematics book

2.Write Boolean expressions for the output from the devices shown in Figure 5.21.

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3.Design electronic devices which produce the following outputs:

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5.Use truth tables to verify that the following pairs of expressions are logically equivalent:

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7. Simplify the following Boolean expressions using the laws of Boolean algebra:

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10.Derive Boolean expressions and truth tables for the circuits shown in Figure 5.22.

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11.Simplify the following Boolean expressions using Boolean algebra:

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12.The truth values of the Boolean expression, X, are given in the following tables. Write X in disjunctive normal form.

Use the laws of Boolean algebra to simplify your expressions.

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Comments

The laws of set algebra & Laws derivable >> in the table 5.1 & 5.2 :

Ans : Commutative laws Ans: Associative laws Ans: Distributive laws Ans: Identity laws Ans: Complement laws Ans: Absorption laws Ans: Minimization laws Ans: De Morgan’s laws

Matrix algebra

Matrices provide a means of storing large quantities of information in such a way that each piece can be easily identified and manipulated. They permit the solution of large systems of linear equations to be carried out in a logical and formal way so that computer implementation follows naturally. Applications of matrices extend over many areas of engineering including electrical network analysis and robotics. 1-BASIC DEFINITIONS Matrix is a rectangular pattern or array of numbers. For example: are all matrices. Note that we usually use a capital letter to denote a matrix, and enclose the array of numbers in brackets. To describe the size of a matrix we quote its number of rows and columns in that order so, for example, an r × s matrix has r rows and s colu...

Discrete mathematics

It's about Discrete mathematics in this book #Anthony Croft, Engineering Mathematices, 5e (2017) So i will choose exercise 5.2 #7 #8 #9 to slow everyone: 7 . The sets A, B and C are given by A = {1, 3, 5, 7, 9}, B = {0, 2, 4, 6} and C = {1, 5, 9} and the universal set, E = {0,1, 2, . . . ,9}. (a) Represent the sets on a Venn diagram. (b) State A ∪ B. (c) State B ∩ C. (d) State E ∩ C. (e) State not A. (f) State not B ∩not C. (g) State not (B ∪C). Ans : a ) Represent the sets on a Venn diagram : The set containing all the numbers of interest is called the universal set, E. E is represented by the rectangular region. Sets A , B and C are represented by the interiors of the circles and it is evident that 1 , 3, 5, 7 and 9 are members of A while 0, 2, 4, and 6 are members of B that 1, 5 and 9 are members of C....

Hoang Lihuo

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