Question

Let A={10,15,20,25,30,35,40,45,50},B={1,5,10,15,20,30}and C={7,8,15,20,35,45,48}, verify A-(B+C)=(A-B) +(A-C)

Answer 1

Answer:

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11th

Maths

Sets

Operations on Sets

Let A = 10, 15, 20, 25, 30,...

MATHS

Let A = {10, 15, 20, 25, 30, 35, 40, 45 } 50 , B = { 1, 5,10,15, 20, 30} and C = { 1, 5,15, 20, 35, 45, }. Verify A∖(B∩C)=(A∖B)∪(A∖C).

December 26, 2019avatar

Anshika Delhi

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ANSWER

The given sets are A={10,15,20,25,30,35,40,45,50}, B={1,5,10,15,20,30} and C={1,5,15,20,35,45}

Let us first find A∖(B∩C) as follows:

A∖(B∩C)={10,15,20,25,30,35,40,45,50}∖({1,5,10,15,20,30}∩{1,5,15,20,35,45})

={10,15,20,25,30,35,40,45,50}∖{1,5,15,20}={10,25,30,35,40,45,50}........(1)

Now we find (A∖B)∪(A∖C) as follows:

(A∖B)∪(A∖C)

=({10,15,20,25,30,35,40,45,50}∖{1,5,10,15,20,30})∪({10,15,20,25,30,35,40,45,50}∖

{1,5,15,20,35,45})

={25,35,40,45,50}∪{10,25,30,40,50}={10,25,30,35,40,45,50}........(2)

Since equation 1 is equal to equation 2,

Hence, A∖(B∩C)=(A∖B)∪(A∖C)

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Answer 2

Answer:

A={8,10,12,14,16,18,20} எனில் n(A) காண்க