Question

7. State the distributive laws of boolean algebra. How do they differ from the distributive laws of ordinary
algebra ?​

Answer 1

Distributive law of boolean algebra

1) x(y+z) = xy + xz

2) x + yz = (x+y) (x+z)

• Both laws exist in boolean algebra.

Distributive law of ordinary algebra

● x(y+z) = xy + xz

• This law exists in ordinary algebra.

prove -

let x = 1

y = 2

z = 3

LHS

1 ( 2 + 3 )

1 × 5

= 5

RHS

1×2 + 1×3

2 + 3

=5

Hence, LHS = RHS

It can be seen that x(y+z) = xy + xz its exist.

● x + yz = (x+y) (x+z)

• This law does not exist in ordinary algebra.

prove -

let x = 1

y = 2

z = 3

LHS

1 + 2×3

1 + 6

= 7

RHS

(1 + 2) (1 + 3)

3 × 4

=12

LHS not equals to RHS

It doesn't exists in ordinary algebra.