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John was asked to give an example of a set - Junior Cycle Mathematics - Question 5 - 2014
Question 5
John was asked to give an example of a set. He said: "The set of good websites." Explain why this is not a set. The sets $U$, $A$, and $B$ are defined as follows: $... show full transcript
Worked Solution & Example Answer:John was asked to give an example of a set - Junior Cycle Mathematics - Question 5 - 2014
Step 1
Explain why this is not a set.
Answer
The phrase "the set of good websites" is not a well-defined set because the term 'good' is subjective. What constitutes a 'good' website can vary from person to person. Therefore, it's impossible to determine a clear and objective list of websites that would belong to this set. A proper set must have a clear definition that applies universally.
Step 2
Use these sets to fill in the Venn diagram.
Answer
To fill in the Venn diagram:
- Set (multiples of 2): {2, 4, 6, 8, 10}
- Set (multiples of 3): {3, 6, 9}
- The number 6 is the overlap since it is a multiple of both 2 and 3.
- Thus, the filled Venn diagram shows:
- Set with elements {2, 4, 6, 8, 10}
- Set with elements {3, 6, 9}
- The overlapping section has the element {6}.
Step 3
Using your Venn diagram, find the smallest number that is both a multiple of 2 and a multiple of 3 (the least common multiple).
Answer
To find the least common multiple (LCM) of 2 and 3, we can identify the first multiples of each:
- The multiples of 2 are: 2, 4, 6, 8, 10...
- The multiples of 3 are: 3, 6, 9... The smallest common multiple is 6; hence, the least common multiple of 2 and 3 is 6.