Question

Which of the following statements are always true? Justify your answers. a. If A + B = C, then AD' + BD' = CD' b. If A'B + A'C = A'D, then B + C = D c. If A + B = C, then A + B + D = C + D d. If A + B + C = C + D, then A + B = D

Answer 1

a. True

B. False

C. True

D. False

Explanation:

a.) A+B = C then AD' + BD' = CD'

AD'+BD' = D'(A+B)

and we already have that A+B = C

such that D'C = C'D

this statement is true

b.) A'B + A'C = A'D then B+C = D

let's have A = 1 and B= 0, C= 0 and D = 1

A'(0) + A'(0) = 1(1)

0+0 = 1

0 = 1

This is false because 0 is not equal to 1

c.) A+ B=C then A+B+D= C+D

If A+B+D= C+D

Then A+B=C

The statement is true

d.) A+B+C=C+D

A+B = D

let's equate A = 0

B= 0

C= 1

D= 1

from a+b = D

We have

0+0 = 1

0 is not equal to 1

The statement is false

Explanation:

Answer 2

a. True

B. False

C. True

D. False

Explanation:

a.) A+B = C then AD' + BD' = CD'

AD'+BD' = D'(A+B)

and we already have that A+B = C

such that D'C = C'D

this statement is true

b.) A'B + A'C = A'D then B+C = D

let's have A = 1 and B= 0, C= 0 and D = 1

A'(0) + A'(0) = 1(1)

0+0 = 1

0 = 1

This is false because 0 is not equal to 1

c.) A+ B=C then A+B+D= C+D

If A+B+D= C+D

Then A+B=C

The statement is true

d.) A+B+C=C+D

A+B = D

let's equate A = 0

B= 0

C= 1

D= 1

from a+b = D

We have

0+0 = 1

0 is not equal to 1

The statement is false