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Home » Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L–(M∪N) = (L–M)∩(L–N).
Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L–(M∪N) = (L–M)∩(L–N).
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L–(M∪N) = (L–M)∩(L–N).

Solution:

As per the question,

\mathrm{L}=\{1,2,3,4\}, \mathrm{M}=\{3,4,5,6\} and \mathrm{N}=\{1,3,5\}

We need to verify:

\begin{array}{l} L-(M \cup N)=(L-M) \cap(L-N) \\ M=\{3,4,5,6\}, N=\{1,3,5\} \Rightarrow M \cup N=\{1,3,4,5,6\} \\ L=\{1,2,3,4\} \text { and } M \cup N=\{1,3,4,5,6\} \\ \Rightarrow L-(M \cup N)=\{2\} \ldots \ldots \dots \dots \dots . .(i) \\ L=\{1,2,3,4\} \text { and } M=\{3,4,5,6\} \Rightarrow L-M=\{1,2\} \\ L=\{1,2,3,4\} \text { and } N=\{1,3,5\} \Rightarrow L-N=\{2,4\} \\ L-M=\{1,2\} \text { and } L-N=\{2,4\} \\ \Rightarrow(L-M) \cap(L-N)=\{2\} \ldots \ldots \ldots . . . . \text { (ii) } \end{array}

From eq.(i) and eq.(ii),

We get,

L-(M \cup N)=(L-M) \cap(L-N)

As a result, verified

i

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