# Let A = {3, 5, 7}, B = {2, 3, 4, 6} and C = {2, 3, 4, 5, 6, 7, 8} (i) Verify (A ∩ B)' = A' ∪ B' (ii) Verify (A ∪ B)' = A' ∩ B'

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by Deleted account

• Brainly User
2016-03-28T06:32:21+05:30

Solution

(i) (A ∩ B)' = A' ∪ B'

L.H.S. = (A ∩ B)'

A ∩ B = {3}

(A ∩ B)' = {2, 4, 5, 6, 7, 8}     ……………….. (1)

R.H.S. = A' ∪ B'

A’ = {5, 7, 8}

B’ = {2, 4, 6}

A’∪B’ = {2, 4, 5, 6, 7, 8}     ……………….. (2)

From (1) and (2), we conclude that;

(A ∩ B)' = (A' ∪ B')

(ii) (A ∪ B)' = A' ∩ B'

L.H.S. = (A ∪ B)'

A∪B = {2, 3, 4, 5, 6, 7}

(A ∪ B)' = {8}     ……………….. (1)

R.H.S. = A' ∩ B'

A' = {2, 4, 6, 8}

B' = {5, 7, 8}

A' ∩ B' = {8}     ……………….. (2)

From (1) and (2), we conclude that;

(A ∪ B)' = A' ∩ B'

2016-03-28T07:09:30+05:30

(i) (A ∩ B)' = A' ∪ B'

L.H.S. ⇒ (A ∩ B)'

⇒A ∩ B = {3}

(A ∩ B)' = {2, 4, 5, 6, 7, 8}    -----(1)

R.H.S. ⇒ A' ∪ B'

A’ = {5, 7, 8}

∴B’ = {2, 4, 6}

A’∪B’ = {2, 4, 5, 6, 7, 8}    ---- (2)

From (1) and (2), we get,

∴(A ∩ B)' = (A' ∪ B')

(ii) (A ∪ B)' = A' ∩ B'

L.H.S. ⇒ (A ∪ B)'

A∪B = {2, 3, 4, 5, 6, 7}

⇒(A ∪ B)' = {8}    ----- (3)

R.H.S. ⇒ A' ∩ B'

A' = {2, 4, 6, 8}

B' = {5, 7, 8}

⇒A' ∩ B' = {8}  ----(4)

From (3) and (4), we get;

∴(A ∪ B)' = A' ∩ B'