Question

solve this math plz ........and i will surely mark u as brainliest. ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution

given :

(universal set) ξ = { 1,2,3,4,5,6,7,8,9 }

A = { 1,2,3,4,6,7,8 }

B = { 4,6,8 }

to find:

(1) A '

A ' = ξ - A

A ' = { 5 , 9 }

(2) B '

B ' = ξ - B

B ' = { 1,2,3,5,7,9 }

(3) A ∪ B

A ∪ B = { 1 , 2,3,4,6,7,8 }

(4) A ∩ B

A ∩ B = { 4,6,8 }

(5) A - B

A - B = {1,2,3,7}

(6) B - A

B - A = φ

(7) ( A ∩ B) '

( A∩B) ' = ξ - ( A ∩ B )

(A ∩ B) ' = { 1,2,3,5,7,9 }

(8) A ' ∪ B '

A ' ∪ B ' = {1,2,3,5,7,9 }

Verify that :

(a) ( A∩B )' = A' ∪ B'

LHS = ( A∩B )'

       = { 1,2,3,5,7,9 }

RHS = A' ∪ B'

       = { 1,2,3,5,7,9 }

LHS = RHS . verified.

(b) n (A) + n(A') = n (ξ)

LHS = n (A) + n(A')

       = 7 + 2

       = 9

RHS = n (ξ)

        = 9

LHS = RHS . verified.

(c) n (A∩B) + n((A∩B)') = n (ξ )

LHS = n ( A∩B ) + n ((A∩B)')

       = 3   +  6

       = 9

RHS = n ( ξ)

       = 9

LHS = RHS , verified.

(d) n(A-B) + n(B-A) + n ( A∩B ) = n ( A∪B )

LHS = n(A-B) + n(B-A) + n( A ∩ B)

       = 4   +  0   +  3

       = 7

RHS = n ( A ∪ B )

       = 7

LHS = RHS . verified.