Question

5)
If A = {1, 2, 3,4}, B = {3,4,5,6},
C = {4, 5, 6, 7, 8} and universal set
X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10), then verify
the following:
i)
AU(BNC) = (AUB) n (AUC)
ii)
An(BUC) = (ANB) U (AUC)
if (AUB)' = FA'NBX
iv) (ANB)' = A'UB'
v) A = (ANBU (ANB')
vi) B = (ANB)U (ANB)
vii) (AUB) = (A-B) U (ASB) U (B-A)
viii) A (BAC) = (ANB) A (ANC)
ix) n (AUB) = n(A) + n(B) - n(ANB)
x) n (B) = (A'NB) + n(ANB)​

Answer 1

Answer:

Tofind:−

we need to verify that :-

A∩(B ∪ C) = (A ∩ B) ∪ (A ∪ C)

\large\bf\underline{Given:-}

Given:−

A= {1,2,3,4}

B = {3,4,5,6}

C = {4, 5, 6, 7, 8}

universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

\huge\bf\underline{Solution:-}

Solution:−

A= {1,2,3,4}

B = {3,4,5,6}

C = {4, 5, 6, 7, 8}

∪ = X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(B ∪ C) = { 3 ,4 ,5 ,6 ,7 ,8 } .....1)

Intersection from 1) and set A we get,

A∩(B ∪ C) = { 3 ,4 } .....2)

(A ∩ B) = { 3 , 4 } ......3)

(A ∪ C) = { 1 ,2 ,3 ,4, 5 ,6 ,7 ,8 } .....4)

Now,

Union set from 3) and 4)

(A ∩ B) ∪ (A ∪ C) = {1 , 2 ,3, 4, 5 ,6, 7, 8 } ......5)

Now,

✝️ verification :-

A∩(B ∪ C) = (A ∩ B) ∪ (A ∪ C)

{ 3 ,4 } ≠ { 1 ,2 ,3 ,4 ,5 ,6 ,7 ,8}

So,

A∩(B ∪ C) ≠ (A ∩ B) ∪ (A ∪ C)

hu.