Question

Boolean algebra show that (a+b)(b+c)(c+a)=ab+bc+ca

Answer 1

Question:If a, b,c are positive then show that bc/b+c+ca/c+a+ab/a+b<(a+b+c)1/2

Step-by-step explanation:

Answer 2

Answer:

It is proven that   (a + b) (b + c) (c + a) = ab + bc +ca

Step-by-step explanation:  

Given problem

show that (a+b) (b+c) (c+a) = ab+bc+ca  by using Laws of Boolean Algebra    

Take  LHS  = (a+ b) (b+c) (c+a )

[ from commutative law  A +B = B+ C ⇒ (b+ c) = (c + b) ]  

     = (a + b) (c + b) (c + a)  

[ from distributive law A+ (B.C ) = (A+B) (A+C) ⇒ (b+c) (a+c) = (c +ab) ]                

    = (a+b) ( c+ ab)          

    =  a(c+ab) + b(c+ ab)  

    = ac + aab + bc + abb  

[ from identity law  A.A = A  ⇒   a.a = a  and  b.b = b ]

   = ac + ab + bc +ab

   = ac + bc + ab + ab

[ from identity law  A.A = A  ⇒   ab . ab = ab ]  

  = ac + bc + ab = ab + bc +ca = RHS

                         LHS = RHS

therefore it is proven that (a + b) (b + c) (c + a) =  ab + bc +ca