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Home » If A = {1, 2, 3}, B = {4}, C = {5}, then verify that: (iii) A x (B – C) = (A x B) – (A x C)
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that: (iii) A x (B – C) = (A x B) – (A x C)
CBSE | Class 11 | Exercise 2.2 | Maths | RD Sharma | Relations
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that: (iii) A x (B – C) = (A x B) – (A x C)

(iii) A × (B − C) = (A × B) − (A × C)

Let us consider LHS: (B − C)

\left( B\text{ }-\text{ }C \right)\text{ }=~\varnothing

A\text{ }\times \text{ }\left( B\text{ }-\text{ }C \right)\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3 \right\}\text{ }\times \varnothing

A\text{ }\times \text{ }\left( B\text{ }-\text{ }C \right)=~\varnothing

Now, RHS

\left( A\text{ }\times \text{ }B \right)\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3 \right\}\text{ }\times \text{ }\left\{ 4 \right\}

\left( A\text{ }\times \text{ }B \right)=\text{ }\left\{ \left( 1,\text{ }4 \right),\text{ }\left( 2,\text{ }4 \right),\text{ }\left( 3,\text{ }4 \right) \right\}

\left( A\text{ }\times \text{ }C \right)\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3 \right\}\text{ }\times \text{ }\left\{ 5 \right\}

\left( A\text{ }\times \text{ }C \right)=\text{ }\left\{ \left( 1,\text{ }5 \right),\text{ }\left( 2,\text{ }5 \right),\text{ }\left( 3,\text{ }5 \right) \right\}

\left( A\text{ }\times \text{ }B \right)\text{ }-\text{ }\left( A\text{ }\times \text{ }C \right)\text{ }=~\varnothing

∴ LHS = RHS

 

i

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