Question 1025806: By drawing a Venn diagram, replace the expression with one involving at most one union and the complement symbol applied only to R,S, and T. Simplify the expression. (' is the complement)
(R∩S)∪(S∩T)∪(R∩S'∩T')
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
(R∩S)∪(S∩T)∪(R∩S'∩T')
R∩S is made up of the two regions which are
in common to the circles R,S. They are
regions 2&5, So we can substitute 2&5 for R∩S.
(2&5)∪(S∩T)∪(R∩S'∩T')
S∩T is made up of the two regions which are
in common to the circles S,T. They are
regions 5&6, So we can substitute 5&6 for S∩T.
(2&5)∪(5&6)∪(R∩S'∩T')
R∩S'∩T' is a little more complicated. There are
primes (tic marks) on S and T, indicating
complements. That means that R∩S'∩T' is the
part of R that is NOT part of S, and also NOT
part of T. That is only the left part of circle
R, the one region 1, because it is the only part
of R that is NOT part of the other two circles.
So we replace R∩S'∩T' by 1.
(2&5)∪(5&6)∪(1)
So we end up with the 4 regions 1&2&5&6, so
(R∩S)∪(S∩T)∪(R∩S'∩T') = 1&2&5&6
Regions 1 and 2 are the parts of R that are not parts
of T. So that's (R∩T')
We only need to union that with regions 5 and 6.
Regions 5 and 6 are the regions common to S and T
(R∩T')∪(S∩T)
Edwin
|
|
|
