Introduction: The focus in Grade 11 is on three-set problems. The key is to start filling the Venn diagram from the very center (the intersection of all three sets) and work your way outwards.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Shade): In a Venn diagram for three sets A, B, C, shade the region representing A∩B∩C.

• Prompt 2 (Shade): Shade the region representing A∪B.

• Prompt 3 (Shade): Shade the region representing C′.

• Prompt 4 (Describe): Describe in words the region (A∩B)∩C′.

• Prompt 5 (Calculate): In a Venn diagram, the number of elements in region A only is 10, B only is 12, and A∩B is 5. Find n(A∪B).

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Task): A group of 50 students were asked about the languages they speak. 25 speak Sinhala, 20 speak Tamil, and 18 speak English. 8 speak Sinhala and Tamil, 7 speak Tamil and English, 10 speak Sinhala and English, and 5 speak all three. Represent this in a Venn diagram.

• Prompt 2 (Interpret): From the diagram, find how many students speak only Sinhala.

• Prompt 3 (Interpret): How many students speak exactly two languages?

• Prompt 4 (Interpret): How many students speak none of these languages?

• Prompt 5 (Notation): Write the set of students who speak English but not Sinhala, using set notation.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Problem Solve): In a survey of 100 people, it was found that everyone reads at least one of three newspapers A, B, C. 60 read A, 40 read B, 50 read C. 20 read A and B, 15 read B and C, 25 read A and C. Find the number of people who read all three newspapers.

• Prompt 2 (Shade): Shade the region representing (A∪C)′∪B.

• Prompt 3 (Explain): Explain using a Venn diagram why n(A∪B)=n(A)+n(B)−n(A∩B).

• Prompt 4 (Problem Solve): Out of 200 candidates, 120 passed the Maths test, 110 passed the Science test and 90 passed the English test. 40 candidates failed in all three subjects. If 70 passed in exactly two subjects, how many passed in all three subjects?

• Prompt 5 (Logic): All students who play cricket also play volleyball. 15 students play cricket, 25 play volleyball, and 10 play football. 5 play all three sports. 8 play volleyball and football. Draw a Venn diagram to represent this information.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Derive): Write down the Principle of Inclusion-Exclusion for three sets: n(A∪B∪C)=...

• Prompt 2 (Proof): Use Venn diagrams to prove the De Morgan's Law: (A∪B)′=A′∩B′.

• Prompt 3 (Challenge): In a school, 20 teachers teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both subjects. How many teach Physics? Now, if 15 teachers teach Physics or Chemistry, with 5 teaching both, and there are no teachers who teach all three subjects, how many teachers are there in total?

• Prompt 4 (Algebra & Sets): Let E be the set of positive integers less than 30. Let A = {multiples of 3}, B = {multiples of 5}, C = {factors of 24}. Find n((A∩C)∪B′).

• Prompt 5 (Problem Solve): In a class, the number of students who like apples is twice the number who like only bananas. The number who like both is 5. The number who like neither is 3. If there are 30 students in the class and 18 like apples, find the number of students who like only bananas.