Question

If u equals to {1, 2, 3, 4,.....,10} is the universal set for the two sets a={2,3,4,5} and b={1,2,3,4,5,6} then verify that (a u b)" equals to a" n b"

Answer 1

Step-by-step explanation:

Given

     a = { 2, 3, 4, 5 }   and   b = { 1, 2, 3, 4, 5, 6 }

Then

     a ∪ b = [ everything in one or the other ]

               = { 1, 2, 3, 4, 5, 6 }

so

   ( a ∪ b )' = [ the complement, so everything in u that's not in a∪b ]

                  = { 7, 8, 9, 10 }.         ...(*)

Also

     a' = { 1, 6, 7, 8, 9, 10 }    and    b' = { 7, 8, 9, 10 }

so

     a' ∩ b' = [ those elements in both a' and b' ]

                 = { 7, 8, 9, 10 }.          ...(**)

The sets at (*) and (**) are the same, verifying the relationship

    ( a ∪ b )' = a' ∩ b'.

Hope this helps.

Answer 2

aub not = anb

234516 not=2345