Question

Prove that :(A-B)UB=AUB

Answer 1

hey,
Let A={1,2,3,4,5}
B={1,2,3}
A-B={4,5} .........(the elements which are in A but not in B)
by taking L.H.S
(A-B)U B={1,2,3,4,5}→1
by taking R.H.S
AUB={1,2,3,4,5}→2
From 1 and 2
(A-B)U B= AUB
L.H.S=R.H.S
Hence proved

Answer 2

Answer:

The proof is explained step wise below :

Step-by-step explanation:

To show : (A - B) U B = A U B

We need to show two things :  

a) (A - B) U B is a subset of A U B  

b) A U B is a subset of (A - B) U B

To show a) :  

Let x ∈ (A - B) U B

Then, x ∈ A - B or x ∈ B  

If x ∈ A - B then x ∈ A and x ∈ B', from which is follows that x ∈ A U B  

If x ∈ B then x ∈ A U B, from which it follows that x ∈ A U B  

Therefore, (A - B) U B is a subset of A U B  

To show b) :

Let x ∈ A U B  

Then, x ∈ A or x ∈ B.  

If x ∈ A then x ∈ A - B, from which it follows that x ∈ (A - B) U B  

If x ∈ B then x ∈ A U B  

Therefore, A U B is a subset of (A - B) U B  

This proves that (A - B) U B = A U B

Hence Proved.