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Question

If X={1,2,3,4,5,6,7,8,9,10} is the universal set andA={1,2,3,4},B={2,4,6,8},C={3,4,5,6} verify the following.
(a) A(BC)=(AB)C
(b)A(BC)=(AB)(AC)
(c) (A)=A

A
Only a is true
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B
Only b and c are true
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C
Only a and b are true
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D
All three a,b and c are true.
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Solution

The correct option is D All three a,b and c are true.
given
X={1,2,3,4,5,6,7,8,9,10},A={1,2,3,4},B={2,4,6,8},C={3,4,5,6}

now from the given data

AB={1,2,3,4,6,8},BC={2,3,4,5,6,8}

Now A(BC)={1,2,3,4,5,6,8}and(AB)C={1,2,3,4,5,6,8}

A(BC)=(AB)C={1,2,3,4,5,6,8}

AB={2,4},AC={3,4},BC={2,3,4,5,6,8}

Now A(BC)={2,3,4}and(AB)(AC)={2,3,4}

A(BC)=(AB)(AC)={2,3,4}

A={5,6,7,8,9,10}

therefore (A)={1,2,3,4}=A

therefore all three a,b,c are true

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