Please help with all of them and show work please Simplify the following expressions F(x, y, z) = xy + x’y’z’ + x’yz’ F(x, y, z) = x’yz + xy’z + x’yz’ F(x, y, z) = xy’z’ + xz + x’y’z F(w, x, y, z) =x’z + w’xy’ + w(x’y + xy’) F(w, x, y, z) =w’x’y’z’ + wy’z’ + x’yz’ + w’xyz + xy’z
Please help with all of them and show work please Simplify the following expressions F(x, y, z) = xy + x’y’z’ + x’yz’ F(x, y, z) = x’yz + xy’z + x’yz’ F(x, y, z) = xy’z’ + xz + x’y’z F(w, x, y, z) =x’z + w’xy’ + w(x’y + xy’) F(w, x, y, z) =w’x’y’z’ + wy’z’ + x’yz’ + w’xyz + xy’z
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter6: Modularity Using Functions
Section6.4: A Case Study: Rectangular To Polar Coordinate Conversion
Problem 9E: (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by...
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Please help with all of them and show work please
Simplify the following expressions
-
- F(x, y, z) = xy + x’y’z’ + x’yz’
- F(x, y, z) = x’yz + xy’z + x’yz’
- F(x, y, z) = xy’z’ + xz + x’y’z
- F(w, x, y, z) =x’z + w’xy’ + w(x’y + xy’)
- F(w, x, y, z) =w’x’y’z’ + wy’z’ + x’yz’ + w’xyz + xy’z
Expert Solution
Step 1
- F(x, y, z) = xy + x’y’z’ + x’yz’
Using Boolean algebra, we can simplify the expression using De Morgan's laws and the distributive property.
xy + x’y’z’ + x’yz’
= xy + x’(y’z’) + (x’y)z’ (distributive property)
= xy + (x’ + x’y)z’ (De Morgan's laws)
= xy + x’z’ (De Morgan's laws)
So, the simplified expression is: F(x, y, z) = xy + x’z’
- F(x, y, z) = x’yz + xy’z + x’yz’
Using Boolean algebra, we can simplify the expression using the distributive property.
x’yz + xy’z + x’yz’
= (x’y + xy’)z + x’yz’ (distributive property)
= z(x’y + xy’) + x’yz’ (distributive property)
= z + x’yz’ (De Morgan's laws)
So, the simplified expression is: F(x, y, z) = z + x’yz’
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