Let the sets R,S be defined as following finite sets
R= {xÎZ+ / x is divisible by 2 but less than 20}
S= {yÎ Z+ / y is divisible by 3 but less than 30}
For the sets R and S prove the following set identities
i)A∩B = B∩A
ii)A—B ≠ B—A
Hi
Is ?
This is a general result : is the set which contains all the elements which lie in both and . What does it mean for ?
To show that two sets are not equal, you only need to find an element which is in only one of the two sets. Can you find an element of which is not in ? (to help you, you can write down the elements of , of , of and of )ii)A—B ≠ B—A
Hope that helps
A = {2.4.6.8.10.12.14.16.18}
B={3.6.9.12.15.18}
intersection symbol is not there so just i say...
left/right hand side -LHS/RHS in (i)
LHS={6.12.18}RHS={6.12.18}
that is the first one is equal.
A-B= {2,3,4,8,9,10,14,15,16}
B-A= {3,9,15}
therefore the second one also proved.