2 Answers

find the complement of P…

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MATHS

Given U = {x: x is a positive integer less than 15}

and P = {x: x is even number from 1 to 14},

find the complement of P

  • A. {1, 3, 5, 7, 9, 11, 13, 15}
  • B. {2, 3, 5, 7, 9, 11, 13}
  • C. {1, 3, 5, 7, 9, 11, 13}
  • D. {2, 3, 5, 7, 11, 15}

QUICK ANSWER…

C

SOLUTION 

The complement of a set is another set containing the element(s) which are present in the universal set, but absent in the set.

Or, complement of a set is another set containing elements which when added to the original set makes it equal to the universal set.

So, from the question,

The universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

A sub-set P = {2, 4, 6, 8, 10, 12, 14}

Therefore, complement of P = {1, 3, 5, 7, 9, 11, 13}

Now for the right answer to the above question:

  1. Option A is incorrect. x is less than 15, not equal to 15.
  2. Option B is incorrect. 2 is present in set P. also, 1 is missing here.
  3. C is correct.
  4. D is not the correct answer. 2 and 15 are wrong entries.

KEY-POINTS…

You may please note these/this:

  • The elements in the universal set is less than, and not equal to 15.
  • The complement of a set is simply another set that when added to it, makes it equal to the universal set.
  • The complement of a set can be imagined as another set that completes it and makes it equal to the universal set.

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/ culled from 2016 JAMB-UTME mathematics past question 20 /

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