Discrete Mathematics Sets Question

Question

Prove that : 

A △ B = ( A ∪ B ) - ( A ∩ B )  

Comments

i need to show that LHS is a subset of RHS

and RHS is a Subset of LHS

by this logic it will be proved sir :((((

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Your question is like 

prove that 

8-2 = 5+3-2

 

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here LHS is subset of RHS and Vice versa because For Every subset 'A'  'A' and $\phi$ is called trivial subset of A.

Answer 1

The symmetric difference using Venn diagram of two subsets A and B is a sub set of U, denoted by A △ B

and is defined by A △ B = (A – B) ∪ (B – A) Let A and B are two sets.

The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B.

Thus, A △ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B}

or, A △ B = {x : [x ∈ A and x ∉ B] or [x ∈ B and x ∉ A]}

A △ B = (A – B) ∪ (B – A)

{1,3} = {1} ∪ {3}

{1,3} = {1,3}

 

"Hence Proved"