Question

It A={2,3₂6) B= {1,5,10) c= {3,5,6) D = (1,2,10)
Prove (Anc) x (BnD) = (AxB) n (CXD)​

Answer 1

Given A={2,3,6},B={1,5,10},C={3,5,6} and D={1,2,10}

• Then, AnC= {2,3,6}n{3,5,6}

= {3,6}

• BnD={1,5,10}n{1,2,10}

={1,10}

• AxB={2,3,6}x{1,5,10}

={(2,1),(2,5),(2,10),(3,1),(3,5),(3,10),(6,1),(6,5),(6,1)}

• CxD={3,5,6}x{1,2,10}

={(3,1),3,2),(3,10),(5,1),(5,2),(5,10),(6,1),(6,2),(6,10)}

Now (AnC) x (BnD) = {(3,1),(3,10),(6,1),(6,10)}

and (AxB) n (CxD)= {(3,1),(3,10),(6,1),(6,10)}

Therefore (AnC) x (BnD) = (AxB) n (CxD)

Hence proved