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Home » If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (i) (A U B)’ = A’ ∩ B’ (ii) (A ∩ B)’ = A’ U B’
If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (i) (A U B)’ = A’ ∩ B’ (ii) (A ∩ B)’ = A’ U B’
CBSE | Class 11 | Exercise 1.5 | Maths | NCERT | Sets
If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (i) (A U B)’ = A’ ∩ B’ (ii) (A ∩ B)’ = A’ U B’

Solution:

Provided that

U \text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,6,7,8,\text{ }9 \right\}

A\text{ }=\text{ }\left\{ 2,\text{ }4,\text{ }6,\text{ }8 \right\}

B\text{ }=\text{ }\left\{ 2,\text{ }3,\text{ }5,\text{ }7 \right\}

(i) \left( A\text{ }\cup \text{ }B)' \right\text{ }=\text{ }\left\{ 2,\text{ }3,\text{ }4,\text{ }5,\text{ }6,\text{ }7,\text{ }8 \right\}'\text{ }=\text{ }\left\{ 1,\text{ }9 \right\}

A'\cap B'=\text{ }\left\{ 1,\text{ }3,\text{ }5,\text{ }7,\text{ }9 \right\}\cap \left\{ 1,\text{ }4,\text{ }6,\text{ }8,\text{ }9 \right\}\text{ }=\text{ }\left\{ 1,\text{ }9 \right\}

As a result, \left( A\text{ }\cup B \right)'\text{ }=\text{ }A'\cap B'.

(ii) (A\cap B)'=\text{ }\left\{ 2 \right\}'=\text{ }\left\{ 1,\text{ }3,\text{ }4,\text{ }5,\text{ }6,\text{ }7,\text{ }8,\text{ }9 \right\}

A'\text{ }\cup \text{ }B'\text{ }=\text{ }\left\{ 1,\text{ }3,\text{ }5,\text{ }7,\text{ }9 \right\}\text{ }\cup \text{ }\left\{ 1,\text{ }4,\text{ }6,\text{ }8,\text{ }9 \right\}\text{ }=\text{ }\left\{ 1,\text{ }3,\text{ }4,\text{ }5,\text{ }6,\text{ }7,\text{ }8,\text{ }9 \right\}

As a result,(A\cap B)'=\text{ }A'\cup\text{ }B'.

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