Question

involution law proof?

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  


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