Question

If A = (x : x = 6n, n€w and n<6}, B = (x: x = 2n, n€N and 2<n<9) and
C={x: x=3n,n€N and 4<n<10), then show that A - (BUC) = (A - B)U (A -C)​

Answer 1

Answer:

A = {30,24,18,12,6,0}

B = {6,8,10,12,14,16}

C = {15,18,21,24,27}

Step-by-step explanation:

GIVEN, A - (BUC) = (A - B)U (A -C)

*(BUC) ={6,8,10,12,14,16}

U{15,18,21,24,27}

*(BUC) = {6,8,10,12,14,15,16,18,21,24,27}

*(A-B) = {30,24,18,12,6,0} - {6,8,10,12,14,16}

*(A-B) = {30,24,18,6,0}

*(A-C) = {30,24,18,12,6,0} - {15,18,21,24,27}

*(A-C) = {30,11,6,0}

*A - (BUC) = {30,24,18,12,6,0} - {6,8,10,12,14,15,16,18,21,24,27}

*A - (BUC) = {30,0}

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

= {30,24,18,6,0}n{30,11,6,0}

= {30,0}

LHS = RHS

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