# Given: U = {Even numbers between 0 and 30}…

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## Given: U = {Even numbers between 0 and 30}, P = {Multiples of 6 between 0 and 30} Q = {Multiples of 4 between 0 and 30}, find (P U Q)’

• A. {0, 2, 6, 22, 26}
• B. {0, 10, 14, 22, 16}
• C. {2, 10, 14, 22, 26}
• D. {2, 4, 14, 18, 26}

C

## SOLUTION…

U = {Even numbers between 0 and 30} = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}

P = {Multiples of 6 between 0 and 30} = {6, 12, 18, 24, 30}

Q = {Multiples of 4 between 0 and 30} = {4, 8, 12, 16, 20, 24, 28}

(P U Q) = union/combination of P and Q = {4, 6, 8, 12, 16, 18, 20, 24, 28, 30},

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(P U Q)’ = elements in the universal set ‘U’ which is not present in (P U Q) therefore,

(P U Q)’ = {2, 10, 14, 22, 26}

### Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is incorrect.
3. C is correct.
4. D is not the correct answer.

## KEY-POINTS…

• U = universal set,
• Even numbers are factors of 2,
• Complement of a set is another set that contains the elements that is present in the universal set but absent in the original set.

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