Question

In: Computer Science

Part #1 Prove the following by using a Truth Table: x + !xy = x +...

Part #1

Prove the following by using a Truth Table:

        x + !xy = x + y

Part #2

Prove the following by using a Truth Table:

        x(!x + y) = xy

Part #3

Simplify the following Boolean expression using Karnaugh maps:

        ABC + ABC + ABC

Part #4

Simplify the following Boolean expression using Karnaugh maps:

        ABC + ABC + ABC

Part #5

Simplify the following Boolean expression using Karnaugh maps:

        ABCD + ABCD + ABCD + ABCD

Part #6

Simplify the following Boolean expression using Karnaugh maps:

        ABCD + ABCD + ABCD + ABCD

Solutions

Expert Solution

Part #1

Prove the following by using a Truth Table:

        x + !xy = x + y

x + !xy = x + y

x + !xy

x

y

!x

!xy

x+!xy

F

F

T

F

F

F

T

T

T

T

T

F

F

F

T

T

T

F

F

T

x + y

x

y

x +y

F

F

F

F

T

T

T

F

T

T

T

T

see the results of the both of the truth table

hence, it is proved

---

Part #2

Prove the following by using a Truth Table:

        x(!x + y) = xy

x(!x + y) = xy

x(!x + y)

x

y

!x

!x +y

x(!x + y)

F

F

T

T

F

F

T

T

T

F

T

F

F

F

F

T

T

F

T

T

xy

x

y

xy

F

F

F

F

T

F

T

F

F

T

T

T

see the results of the both of the truth table

hence, it is proved

---

solved part 1 and part 2

please post part 3, 4,5 & 6 correctly

see the questions repeated expression

(for example it will be ABC +A'BC+AB'C)

the complement part is missing

please post it correctly, love to answer

all the best

please upvote

venereology answered 2 hours ago
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