Question

A={x:1<x<=4 x in N}B={x:0<=x<2 x in W}C={x:x<3 x in N} verify Ax(BUC)=(A times B)uu(AxC)​

Answer 1

A={2,3,4}

B={0,1,2}

C={1,2,3}

A X (B U C)=(A X B) U (A X C)

LHS

{2,3,4} X [{0,1,2} U {123}

= {234} X {0,1,2,3}

= {(2,0),(2,1),(2,2),(2,3)

(3,0),(3,1),(3,2),(3,3,)

(4,0),(4,1),(4,2),(4,3)}

RHS

A X B

={2,3,4} X {0,1,2}

={ (2,0),(2,1),(22)

(30),(31),32

(4,0),(4,1),(4,2) }

A X C

={2,3,4 } X {1,2,3}

={(2,1),(2,2),(2,3)

(3,1),(3,2),(3,3)

(4,1),(4,2),(4,3) }

A X B. U. A X C

={ (2,0),(2,1),(22)

(30),(31),32

(4,0),(4,1),(4,2) }