Draw a venn diagram to represent the above information

Question

Question 1

a) A school for boys has 242 students in Form 4. Information about the student^' participation in sports is as follows:-

• 132 boys play Rugby
• 68 boys play Basketball
• 105 boys play Cricket
• 25 boys play all three sports
• 33 boys play Rugby and Basketball
• 50 boys play Cricket and Basketball
• 30 boys do not play any of these sports

Let the number of students who play Rugby and Cricket be x

i. Draw a Venn diagram to represent the above information

ii. Determine the value of x

iii. How many boys do not play Rugby or Cricket?

iv. How many boys play at most two of the sports?

Question 2

a) By use of Venn diagrams show by shading the region represented by

i. (A ∩ B)' ∩ (A U B)

ii. (A' ∩ B) U (B' ∩ C)

Question3

State whether TRUE or FALSE giving explanations:

a) The empty set is a proper subset of any set.

b) If two sets A and B are disjoint, then A ∩ B = ∅

c) If A ⊇ B and B ⊆ A, then A ∩ B = ∅

d) For any sets A and B, (A U B)' and (A' ∩ B') = (A' U B')

e) Simplify following expression:

                             {((x^-2y^-3)^-1)/(x²)^-1}+{((y^-1)/(x^0.5y^-3))²}