identify the error in the proof Explain why it is an error I

identify the error in the proof. Explain why it is an error. If the statement is true, correct and rewrite the proof. Highlight the correction and explain your reasoning for addressing the problem in this way. If the statement is false or cannot be proven, explain why you reached this conclusion.

Solution

Answer :

The given statement A U ( A - B ) = A U B is not true .

Counter example :

Let A = { 1 , 2 , 3, 4 } and B = { 1, 2 , 5, 7 ,9 }

Then A U B = { 1 ,2 , 3 , 4 , 5 , 7 , 9 } and A - B = { 3 , 4 } and so A U ( A - B ) = { 1 , 2 , 3, 4 } = A

Hence A U B A U ( A - B )