Question

In the boolean algebra verify using truth table (X+Y)'=X'Y' for each X,Y in {0,1}​

Answer 1

Answer:

From the above truth table it is verified that

(X+Y)' = X' • Y'

Answer 2

Answer:

In the Boolean Algebra, the truth table  (X+Y)'=X'Y' for all X, Y in {0,1}

Explanation:

Boolean Algebra:

• Boolean algebra is a branch of mathematics that includes binary variables and deals with operations on logical values.
• Boolean algebra is unique in that it solely deals with the study of binary variables.
• The digital (logic) circuits are analyzed and made simpler using Boolean algebra.
• It is also known as logical algebra or binary algebra.

Boolean Algebra truth table:

When

1 . x =0 y =0  ⇒ x + y = 0

2. x =0 y = 1   ⇒ x + y = 1

3. x =1 y = 0  ⇒ x + y = 1

4. x =1 y =1    ⇒ x + y = 1

Find x'y'

1. x = 0  y = 0 ⇒ x' = 1 y' = 1  

              ⇒  x' y' = 1

2. x =0  y = 1  ⇒ x' = 1 y' =  0

              ⇒ x' y' = 0

3.  x =1 y = 0 ⇒ x' = 0 y' =  1

               ⇒ x' y' = 0

4. x =1 y =1   ⇒ x' = 0 y' =  0

              ⇒ x' y' = 0

Find (x + y)'

1. x + y = 0   ⇒ (x + y)' = 1

2. x + y = 1  ⇒ (x + y)' = 0

3. x + y = 1   ⇒  (x + y)' = 0

4 . x + y = 1  ⇒ (x + y)' = 0

Therefore,

(X + Y)' = X' Y' are identical.

Truth table has been given below for each X,Y in {0 ,1}

Final answer:

In the Boolean Algebra the truth table (X+Y)'=X'Y' for all X, Y in {0,1}

#SPJ2