Subjective Type

Given $$A ={1,2,3}, B ={3,4}, C ={4,5,6},$$ then show that $$A\cup \left( B\cup C \right) =\{ 1,2,3,4,5,6\}$$ and $$\left( A\times B \right) \cap \left( B\times C \right) =\{ 3,4\}$$

Solution

Clearly A∪(B∪C)={1,2,3,4,5,6}
Now A×B=(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)
and B× C=(3,4),(3,5),(3,6),(4,4),(4,5),(4,6)
Hence (A×B)∩(B×C)={(3,4)}.

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