Question

Proof involution law

Answer 1

Involution is a mathematical function in which the function f is of its own inverse.

Proof:

If x is considered as the domain of f, then x’ will be the complement of x and (x’)’ will be the complement of x’.

By applying the postulate of complements:-

For all x ∈ B there exists an element x' ∈ B, called the complement of x, such that:-

(a) x + x' = 1

(b) x * x' = 0

Therefore,

x + x' = 1; xx' = 0; x' + (x')' = 1; and x'(x')' = 0

(x')' = (x')' + 0

= (x')' + xx'

= [(x')' + x][(x')' + x']

= [x + (x')'][x' + (x')']

= [x + (x')'] * 1

= [x + (x')'][x + x']

= x + [(x')' • x']

= x + [x' • (x')']    

= x + 0    

= x