Question

2.
v) AU(BUC) vi) A-(BUC) vii)
If u = {2, 3, 4, 5}, A = {2, 4) and B = {3, 4), then verify the following laws.
i) A-B = AB
ii) (ANB)' = A'UB' iii) (AUB)' = A' B'
3.If n(A) = 10, n(B) = 12 and n(An B) = 6, then find n(AUB).
4..If A {2, 3, 4, 5), B= {1, 2, 3) and C = {5,6), then verify
n(AU BUC)+P(A) B)+P( B0C)+ n(COA) = n(A)+ n( B)+P(C)+P(A0 B0C)

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Answer 1

2. U = {2,3,4,5} , A = {2,4} , B = {3,4}

(i) A-B = A n B'

LHS : A-B = {2}

RHS : A n B' = {2}

LHS = RHS Hence,proved.

(ii) (A n B)' = A' U B'

LHS : (A n B)' = {2,3,5}

RHS : (A' U B') = {2,3,5}

LHS = RHS Hence,proved.

(iii) (A U B)' = A' n B'

LHS : (A U B)' = {5}

RHS : A' n B' = {5}

LHS = RHS Hence, proved.

3. n(A) = 10 , n(B) = 12 , n(A n B) = 6

n(A U B) = n(A) + n(B) - n(A n B)

= 10 + 12 - 6 = 16

Hope it helps!!

Thank you ✌️

Answer 2

The union of the sets A and B, denoted by A U B, is the set that contains those elements that are either in A or in B, or in both. ... The intersection of the sets A and B, denoted by A n B, is the set containing those elements in both A and B. A n B = 1x | x ∈ A < x ∈ Bl.