The problem requires us to place the numbers 40, 8, and 15 in the Venn diagram. The left circle represents multiples of 5, the right circle represents multiples of 2, and the intersection represents numbers that are multiples of both 2 and 5.

Discrete MathematicsSet TheoryVenn DiagramsNumber TheoryDivisibility
2025/4/4

1. Problem Description

The problem requires us to place the numbers 40, 8, and 15 in the Venn diagram. The left circle represents multiples of 5, the right circle represents multiples of 2, and the intersection represents numbers that are multiples of both 2 and
5.

2. Solution Steps

First, let's identify the multiples of 5 among the given numbers:
40=5×840 = 5 \times 8, so 40 is a multiple of

5. $8 = 5 \times 1.6$, so 8 is not a multiple of

5. $15 = 5 \times 3$, so 15 is a multiple of

5.
Next, let's identify the multiples of 2 among the given numbers:
40=2×2040 = 2 \times 20, so 40 is a multiple of

2. $8 = 2 \times 4$, so 8 is a multiple of

2. $15 = 2 \times 7.5$, so 15 is not a multiple of

2.
Now, let's place the numbers in the Venn diagram:
The intersection contains numbers that are multiples of both 5 and

2. Among the given numbers, 40 is a multiple of both 5 and 2, and 30 is already there.

The "multiples of 5" circle should contain multiples of 5 that are not multiples of

2. The numbers in the provided list include 40, 15, and

2

5. 40 is already taken into account, 25 is already there, and we have to consider where to put the

1

5. Since 15 is not a multiple of 2 and is a multiple of 5, it must be in the circle of "multiples of 5" only.

The "multiples of 2" circle should contain multiples of 2 that are not multiples of

5. In the given numbers, only 8 is a multiple of 2 but not

5. The number 40 is already taken into account, as well as

3

0. Thus:

- 40 belongs in the intersection, representing multiples of 2 and 5, together with
3

0. - 15 belongs in the "multiples of 5" circle only.

- 8 belongs in the "multiples of 2" circle only.

3. Final Answer

40 goes in the intersection.
15 goes in the "multiples of 5" circle only.
8 goes in the "multiples of 2" circle only.

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