Venn diagram of the equation

Here is the breakdown of the Venn diagram regions based on the previous calculations:

• Region 1: People who like all three beverages (Tea, Coffee, and Juice)

  $$|T \cap C \cap J| = 20$$

• Region 2: People who like only Tea and Coffee (not Juice)

  $$|T \cap C| - |T \cap C \cap J| = 50 - 20 = 30$$

• Region 3: People who like only Tea and Juice (not Coffee)

  $$|T \cap J| - |T \cap C \cap J| = 40 - 20 = 20$$

• Region 4: People who like only Coffee and Juice (not Tea)

  $$|C \cap J| - |T \cap C \cap J| = 30 - 20 = 10$$

• Region 5: People who like only Tea (not Coffee or Juice)

  $$|T| - (|T \cap C \text{ only}| + |T \cap J \text{ only}| + |T \cap C \cap J|) = 120 - (30 + 20 + 20) = 120 - 70 = 50$$

• Region 6: People who like only Coffee (not Tea or Juice)

  $$|C| - (|T \cap C \text{ only}| + |C \cap J \text{ only}| + |T \cap C \cap J|) = 90 - (30 + 10 + 20) = 90 - 60 = 30$$

• Region 7: People who like only Juice (not Tea or Coffee)

  $$|J| - (|T \cap J \text{ only}| + |C \cap J \text{ only}| + |T \cap C \cap J|) = 70 - (20 + 10 + 20) = 70 - 50 = 20$$

• Region 8: People who do not like any of the beverages (outside all circles)

  $$\text{Total people} - |T \cup C \cup J| = 200 - 180 = 20$$

To summarize the regions for a Venn diagram:

• Center (T ∩ C ∩ J): 20
• T and C only: 30
• T and J only: 20
• C and J only: 10
• T only: 50
• C only: 30
• J only: 20
• Outside all circles: 20