The universal set, $U = \{ 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20 \}$. A is the set of prime numbers between 1 and 20. B is the set of factors of 20. (a) List the elements of the set A. A = \{ , , , , , , , , , , , \} (b) List the elements of the set B. B = \{ , , , , , \} (c) Fill in the Venn diagram below placing all elements of U in the correct regions. (d) List the elements of A ∩ B. A ∩ B = \{ , \} (e) Complete the sentence below. If an element is in the region A ∩ B, it has two properties: it is a prime number and it is __________. (f) The number 16 is added to the universal set. Place 16 in the correct region in the Venn diagram in part (e) and explain why you placed it there. Reason:

Junior Cycle Mathematics Sets: The universal set, $U = \{ 1, 2,

The universal set, $U = \{ 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20 \}$ - Junior Cycle Mathematics - Question 6 - 2012

Question 6

$The-universal-set,-$U-=-\{-1,-2,-3,-4,-5,-7,-10,-11,-13,-17,-19,-20-\}$-Junior Cycle Mathematics-Question 6-2012.png$

The universal set, $U = \{ 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20 \}$. A is the set of prime numbers between 1 and 20. B is the set of factors of 20. (a) Lis... show full transcript

Worked Solution & Example Answer:The universal set, $U = \{ 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20 \}$ - Junior Cycle Mathematics - Question 6 - 2012

Step 1

List the elements of the set A.

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Answer

The elements of set A (the prime numbers between 1 and 20) are:

Step 2

List the elements of the set B.

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Answer

The elements in set B (the factors of 20) are:

Step 3

Fill in the Venn diagram below placing all elements of U in the correct regions.

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In the Venn diagram, the regions contain the following:

Set A (left circle): 2, 3, 5, 7, 11, 13, 17, 19
Set B (right circle): 1, 2, 4, 5, 10, 20
Intersection (A ∩ B): 2, 5
Unique to U: 16 not included in A or B.

Step 4

List the elements of A ∩ B.

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The elements of the intersection A ∩ B, which are in both sets A and B, are:

Step 5

Complete the sentence below.

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If an element is in the region A ∩ B, it has two properties: it is a prime number and it is a factor of 20.

Step 6

Explain where to place the number 16.

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Answer

The number 16 is added to the universal set. It is placed outside the circles representing sets A and B, as follows:

It is in U but not prime and is not a factor of 20.

The universal set, $U = \{ 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20 \}$ - Junior Cycle Mathematics - Question 6 - 2012

Worked Solution & Example Answer:The universal set, $U = \{ 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20 \}$ - Junior Cycle Mathematics - Question 6 - 2012

List the elements of the set A.

List the elements of the set B.

Fill in the Venn diagram below placing all elements of U in the correct regions.

List the elements of A ∩ B.

Complete the sentence below.

Explain where to place the number 16.

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