F is the set of factors of 12. (a) List the six elements of the set F. F = { , , , , , } The sets P and S are as follows: P is the set of all prime numbers S is the set of all square numbers (i.e. all numbers n², where n ∈ ℕ). The Venn diagram below shows the sets F, P, and S. (b) Write each of the factors of 12 from part (a) into the correct region in the set F in the Venn diagram.

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F is the set of factors of 12 - Junior Cycle Mathematics - Question 4 - 2018

Question 4

F is the set of factors of 12. (a) List the six elements of the set F. F = { , , , , , } The sets P and S are as follows: P is the set of all prime numbers S is ... show full transcript

Worked Solution & Example Answer:F is the set of factors of 12 - Junior Cycle Mathematics - Question 4 - 2018

Step 1

List the six elements of the set F.

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Answer

The factors of 12 are the numbers that divide 12 without leaving a remainder. The complete list of positive factors of 12 is:

1, 2, 3, 4, 6, 12

Thus, we write:

F = {1, 2, 3, 4, 6, 12}

Step 2

Write each of the factors of 12 from part (a) into the correct region in the set F in the Venn diagram.

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Answer

To place the factors of 12 in the Venn diagram:

F contains the elements: 1, 2, 3, 4, 6, 12.
In the set P (prime numbers): 2 and 3 are prime factors.
In the set S (square numbers): 4 is a square factor (since 2² = 4).

Placement in the Venn diagram:

F will include:
- 2 and 3 in the intersection of F and P.
- 4 in the intersection of F and S.
- 1, 6, and 12 in F only as they do not belong to P or S.

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