Question

A={5,6} , B={4,5,6},C={5,6,7}, show that A×A=(B×B)n(C×C).

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Answer 1

Answer:

We are given

A={1,2,3,4,5,6}; B={4,6,7,8,9,10}

C={4,6,10,12}

(1) proof:

LHS=A u (B n C)={1,2,3,4,5,6} u [{4,6,7,8,9,10} n {4,6,10,12}]

= {1,2,3,4,5,6} u {4,6,10}

={1,2,3,4,5,6,10}------------(1)

RHS= (A u B) n (A u C)

=[{1,2,3,4,5,6} u {4,6,7,8,9,10}] n [{1,2,3,4,5,6} u {4,6,10,12}]

={1,2,3,4,5,6,7,8,9,10} n {1,2,3,4,5,6,10,12}

={1,2,3,4,5,6,10}--------------(2)

LHS=RHS

(2)

LHS=A U (B U C)

.={1,2,3,4,5,6} U [{4,6,7,8,9,10} U {4,6,10,12}]

={1,2,3,4,5,6} U {4,6,7,8,9,10,12}

={1,2,3,4,5,6,7,8,9,10,12}--------------(1)

RHS=(A U B) U (A U C)

=[{1,2,3,4,5,6} U {4,6,7,8,9,10}] U [{1,2,3,4,5,6} U {4,6,10,12}]

={1,2,3,4,5,6,7,8,9,10} U {1,2,3,4,5,6,10,12}

={1,2,3,4,5,6,7,8,9,10,12}-------------(2)

LHS=RHS

Answer 2

Hope my attachment helps you...✌️✌️