Question

Replace the AND operations by ORs and vice versa by applying De Morgan's laws to each of these expressions:

a. F = AB+ (C+ A)D
b. F= AB+C) +D
c. F= ABC + A(B+C)
d.* F= (A+B+C)(A+B+C) (Ā+B+C)
e.* F= ABC + ABC + ĀBC

Answer 1

To replace AND operations with ORs and vice versa, we apply De Morgan's laws. Let's apply De Morgan's laws to each expression: a. F = AB+ (C+ A)D
b. F = AB+C) +D
c. F = ABC + A(B+C)
d. F = (A+B+C)(A+B+C) (Ā+B+C)
e. F = ABC + ABC + ĀBC

Step-by-step explanation:

De Morgan's laws state that the complement of the union of two sets is equal to the intersection of their complements, and vice versa. To replace AND operations with ORs, we apply De Morgan's laws by taking the complement of each term and changing the operation. To replace OR operations with ANDs, we apply De Morgan's laws by taking the complement of each term and changing the operation. Let's apply De Morgan's laws to each expression:

a. F = AB+ (C+ A)D

Applying De Morgan's laws to each term:

• F = AB + (C + A)D
• F = AB + CD + AD

b. F = AB+C) +D

Applying De Morgan's laws to each term:

• F = AB + C + D

c. F = ABC + A(B+C)

Applying De Morgan's laws to each term:

• F = ABC + AB + AC

d. F = (A+B+C)(A+B+C) (Ā+B+C)

Applying De Morgan's laws to each term:

• F = (A + B + C)(A + B + C)(A' B' C')

e. F = ABC + ABC + ĀBC

Applying De Morgan's laws to each term:

• F = ABC + ABC + ĀB + ĀC