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Sets Ncert Solutions Maths class 11th Maths Class 11th Sets

37. 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 $\cup$ B) $'$ = A $'$ ∩ B $'$

(ii) A ∩ B) $'$ = A $'$ $\cup$ B $'$

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Payal Gupta | Contributor-Level 10

4 months ago

37. (i) L.H.S = (A $\cup$ B) $'$ = U – (A $\cup$ B)

= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8) $\cup$ {2,3,5,7}]

= {1,2,3,4,5,6,7,8,9} – {2,3,4,5,6,7,8}

= {1,9}

R.H.S. = A $'$ ∩ B $'$ = [U – A] ∩ [U $\cup$ B]

= $[{1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}]$ ∩ $[{1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}]$

= {1,3,5,7,9} ∩ {1,4,6,8,9}

= {1,9}

? L.H.S. = R.H.S.

(A B) = A ∩ B.

(ii) L.H.S. = (A ∩ B) $'$ = U – (A ∩ B)

= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8} ∩ {2,3,5,7}]

= {1,2,3,4,5,6,7,8,9} – {2}

= {1,3,4,5,6,7,8,9}

R.H.S. = A $'$ $\cup$ B $'$

= [U – A] $\cup$ [U – B]

= [ {1,2,3,4,5,6,7,8,9} – {2,4,6,8}] [ {1,2,3,4,5,6,7,8,9} – {2,3,5,7}]

= {1,3,5,7,9} $\cup$ {1,4,6,8,9}

= {1,3,4,5,6,7,8,9}

? L.H.S. = R.H.S.

...more

37. (i) L.H.S = (A $\cup$ B) $'$ = U – (A $\cup$ B)

= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8) $\cup$ {2,3,5,7}]

= {1,2,3,4,5,6,7,8,9} – {2,3,4,5,6,7,8}

= {1,9}

R.H.S. = A $'$ ∩ B $'$ = [U – A] ∩ [U $\cup$ B]

= $[{1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}]$ ∩ $[{1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}]$

= {1,3,5,7,9} ∩ {1,4,6,8,9}

= {1,9}

? L.H.S. = R.H.S.

(A B) = A ∩ B.

(ii) L.H.S. = (A ∩ B) $'$ = U – (A ∩ B)

= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8} ∩ {2,3,5,7}]

= {1,2,3,4,5,6,7,8,9} – {2}

= {1,3,4,5,6,7,8,9}

R.H.S. = A $'$ $\cup$ B $'$

= [U – A] $\cup$ [U – B]

= [ {1,2,3,4,5,6,7,8,9} – {2,4,6,8}] [ {1,2,3,4,5,6,7,8,9} – {2,3,5,7}]

= {1,3,5,7,9} $\cup$ {1,4,6,8,9}

= {1,3,4,5,6,7,8,9}

? L.H.S. = R.H.S.

(A ∩ B) $'$ = A $'$ $\cup$ B $'$ .

less

37. (i) L.H.S = (A<math><mrow><mo>∪</mo></mrow></math> B)<math><mrow><mo>'</mo></mrow></math> = U – (A <math><mrow><mo>∪</mo></mrow></math>B)= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8)<math><mrow><mo>∪</mo></mrow></math> {2,3,5,7}]= {1,2,3,4,5,6,7,8,9} – {2,3,4,5,6,7,8}= {1,9}R.H.S. = A<math><mrow><mo>'</mo></mrow></math> ∩ B<math><mrow><mo>'</mo></mrow></math> = [U – A] ∩ [U<math><mrow><mo>∪</mo></mrow></math> B]= <math><mrow><mrow><mo> [</mo><mrow><mrow><mo> {</mo><mrow><mn>1</mn><mo>, </mo><mn>2</mn><mo>, </mo><mn>3</mn><mo>, </mo><mn>4</mn><mo>, </mo><mn>5</mn><mo>, </mo><mn>6</mn><mo>, </mo><mn>7</mn><mo>, </mo><mn>8</mn><mo>, </mo><mn>9</mn></mrow><mo>}</mo></mrow><mo>–</mo><mo> {</mo><mn>2</mn><mo>, </mo><mn>4</mn><mo>, </mo><mn>6</mn><mo>, </mo><mn>8</mn><mo>}</mo></mrow><mo>]</mo></mrow></mrow></math> ∩ <math><mrow><mrow><mo> [</mo><mrow><mrow><mo> {</mo><mrow><mn>1</mn><mo>, </mo><mn>2</mn><mo>, </mo><mn>3</mn><mo>, </mo><mn>4</mn><mo>, </mo><mn>5</mn><mo>, </mo><mn>6</mn><mo>, </mo><mn>7</mn><mo>, </mo><mn>8</mn><mo>, </mo><mn>9</mn></mrow><mo>}</mo></mrow><mo>–</mo><mo> {</mo><mn>2</mn><mo>, </mo><mn>3</mn><mo>, </mo><mn>5</mn><mo>, </mo><mn>7</mn><mo>}</mo></mrow><mo>]</mo></mrow></mrow></math>= {1,3,5,7,9} ∩ {1,4,6,8,9}= {1,9}? L.H.S. = R.H.S. (A B) = A ∩ B.  (ii) L.H.S. = (A ∩ B)<math><mrow><mo>'</mo></mrow></math> = U – (A ∩ B)= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8} ∩ {2,3,5,7}]= {1,2,3,4,5,6,7,8,9} – {2}= {1,3,4,5,6,7,8,9}R.H.S. = A<math><mrow><mo>'</mo></mrow></math> <math><mrow><mo>∪</mo></mrow></math>B<math><mrow><mo>'</mo></mrow></math>= [U – A] <math><mrow><mo>∪</mo></mrow></math> [U – B]= [ {1,2,3,4,5,6,7,8,9} – {2,4,6,8}] [ {1,2,3,4,5,6,7,8,9} – {2,3,5,7}]= {1,3,5,7,9}<math><mrow><mo>∪</mo></mrow></math> {1,4,6,8,9}= {1,3,4,5,6,7,8,9}? L.H.S. = R.H.S. (A ∩ B)<math><mrow><mo>'</mo></mrow></math> = A<math><mrow><mo>'</mo></mrow></math><math><mrow><mo>∪</mo></mrow></math> B<math><mrow><mo>'</mo></mrow></math>.

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37. 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 $\cup$ B) $'$ = A $'$ ∩ B $'$

(ii) A ∩ B) $'$ = A $'$ $\cup$ B $'$

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37. 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∪ B)' = A' ∩ B' (ii) A ∩ B)' = A' ∪B'

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37. 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 $\cup$ B) $'$ = A $'$ ∩ B $'$

(ii) A ∩ B) $'$ = A $'$ $\cup$ B $'$