Question

A-B) UB - AUB prove it​

Answer 1

Answer:

To show (A-B) U B = A U B you need to show two things: 

a) (A-B)UB is a subset of AUB and 

b) AUB is a subset of (A-B)UB. 

To show a), let x ε (A-B)UB. 

Then x ε A-B or x ε B 

If x ε A-B then x ε A and x ε B', from which is follows that x ε AUB 

If x ε B then x ε AUB, from which it follows that x ε AUB 

Therefore (A-B)UB is a subset of AUB 

To show b), let x ε AUB 

Then, x ε A or x ε B. 

If x ε A then x ε A-B, from which it follows that x ε (A-B)UB 

If x ε B then x ε AUB 

Therefore, AUB is a subset of (A-B)UB 

This proves that (A-B)UB = AUB. 

Answer 2

$\Large\mathtt\green{ }\huge\underline\mathtt\red{Answer : }$

Let A=[1,2,3,4,5)

B-(1,2.3)

A-B14,5. 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.

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