Tuesday 17 October 2017

Sets

A set is a well-defined collection of objects or elements. Questions on sets may involve concepts such as the universal set, null set, subset, cardinal number, union, intersection and complement. The Venn diagram is a useful tool when solving problems involving sets so it is important to be able to draw a Venn diagram and then use this to solve the questions that follow.

Sample question

U = { Natural numbers from 1 to 10 inclusive }

K = { Factors of 6 }

L= { Even numbers }

(a)Fill in the Venn diagram below:

(i)Use ✔ to indicate whether each of the following statements is true or false. Give a reason for each answer.

K ∩ L = { }

True ø False ø✔

The statement is false because K ∩ L = {2, 6 }

(ii)K ≠ L

True ø✔ False ø

The statement is true as K = {1, 2, 3, 6} and L = {2, 4, 6, 8, 10} which are not equal sets.

(iii)K U L = U

True ø False ø✔

The statement is false because K U L = {1, 2, 3, 4, 6, 8, 10}which does not include the elements 5, 7, 9 that are part of the Universal set.

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