Question

Where do all the numbers belong?

Answer 1

Answer: see attachment

Explanation:

Step 1: Find the sets of A, B, and C and the intersections of the sets.

A: (Factors of 15) = {1, 3, 5, 15}

B: (Odd integers) = {1, 3, 5, 7, 9, 11, 13, 15}

C: (Multiples of 3) = {3, 6, 9, 12, 15}

A ∩ B = {1, 3, 5, 15}

A ∩ C = {3, 15}

B ∩ C = {3, 9, 15}

A ∩ B ∩ C = {3, 15}

Step 2: Plot the intersections first, then the individual sets without repeating any numbers

• Plot A ∩ B ∩ C
• Plot A ∩ B , A ∩ C, and B ∩ C
• Plot A, B, and C
• Plot outside (those not included in any of the sets)

Answer 2

Complete Venn diagram is show in image below.

Explanation:

Given numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

We first find element in each region

From given numbers , numbers that are factors of 15 are 1 , 3, 5 and 15.

Multiple of 3 are 3, 6, 9, 12, 15.

Odd integers are 1, 3, 5, 7, 9, 11, 13, 15

Numbers that are factor of 15 and odd integers are 1, 3, 5, 15

Numbers that are multiple of 3 and odd integers are 9

Numbers that are multiple of 3 , factors of 15 and odd integers = 3, 15

Numbers that are not multiple of 3, not factor of 15 and are not odd number will be outside the circles.