Question

A+BC=(A+B)(A+C) is called
theorem.​

Answer 1

Answer:

associative law

If A, B and C are three variables, then the grouping of 3 variables with 2 variables in each set will be of 3 types, such as (A + B), (B + C) and(C + A).

According to associative law

(A + B + C) = (A + B) +C = A + (B + C) = B + (C + A)

We know that, A + AB = A (according to Absorption law)

Now let’s assume that, x = A + (B + C) and y = (A + B) + C

According to associative law, we need to prove that x = y.

Now, find Ax = A [ A + (B + C) ]

= AA +A (B + C)

= A + AB + AC → since AA = A

= (A+ AB) + AC

= A + AC → since A + AB = A

= A → since A + AC = A

Therefore Ax = A

Similarly, for Bx = B [ A + (B + C) ]

= AB +B (B + C)

= AB + BB + BC

= AB + B + BC → since BB = B

= (B+ BC) + AB

= B + AB → since B + BC = B

= B → since B + AB = B

Using these above equations, we can say that the relation between A, B, C and + operator doesn’t change when multiplied by other variable like x, such as xy = yx = x = y.

yx = ((A + B) + C) x

= (A + B) x + Cx

= (Ax + Bx) + Cx

= (A + B) + C

= y xy = (A + (B + C)) y

= Ay + (B + C) y

= Ay + (By + Cy)

= A + (B + C)

= x

So x = y, which means A + (B + C) = (A + B) + C = B + (A +C)

Answer 2

Your Question Is Wrong .

Correct Question and answer is in the Attachment Bro / Sister .

Hope it helps you.