Goal: Find the value of .Step 1: First, we list the elements of each set based on the universal set .Step 2: We need to evaluate the expression . We start from the inside of the parentheses. First, find the union of sets and .Step 3: Next, find the complement of , denoted by . This is the set of all elements in that are not in .Step 4: Now, find the intersection of set with the set . This is the set of elements that are in both and .Step 5: Finally, find the number of elements, , in the resulting set .Conclusion: The value of is 2.

Goal: Find the elements in the union of set and set .Step 1: First, we identify the elements of sets and from the universal set .Set contains the multiples of 3:Set contains the square numbers:Step 2: Next, we find the union of and , denoted by . This is the set containing all elements that are in , or in , or in both. We combine the elements from both sets and list each unique element once.Conclusion: Therefore, the set is .

First, identify the elements of each set from the universal set .The set of odd numbers is .The set of multiples of 3 is .The set of square numbers is .Next, find the intersection , which is the set of elements that are present in all three sets.By comparing the elements of the three sets, we find that the only common element is 9.

Complete the Venn diagram.

Goal: To find the number of elements in each region of the Venn diagram and complete it.Step 1: Determine the number of elements in the union of sets A and B.We are given the total number of elements in the universal set, , and the number of elements outside of both A and B, .The number of elements in the union of A and B is the total number of elements minus those outside the union.Step 2: Calculate the number of elements in the intersection of sets A and B.We use the formula for the union of two sets: .We are given and . Substituting the known values:So, the number of elements in the intersection is 3.Step 3: Calculate the number of elements in the non-overlapping parts of sets A and B.The number of elements in set A only is the total number in A minus the number in the intersection.The number of elements in set B only is the total number in B minus the number in the intersection.Step 4: State the values to complete the Venn diagram.The value in the region for A only is 9.The value in the intersection of A and B is 3.The value in the region for B only is 7.The value outside both sets is given as 1.Conclusion: The Venn diagram is completed with the values 9 in the A-only region, 3 in the intersection, 7 in the B-only region, and 1 outside both circles.

Question Hub

IGCSE (CAMBRIDGE)|9th and 10th|Extended Maths (0580)

Flash Card Study Notes Previous Year Question Hub Practice Set Question Hub

Question year

Question type

Difficulty level

Select time zone

204 Qs

QUESTION:1

MediumPaper 2Subjective2024

Loading whiteboard...

QUESTION:2

EasyPaper 2Subjective2024

Loading whiteboard...

QUESTION:3

EasyPaper 2Subjective2024

Loading whiteboard...

QUESTION:4

HardPaper 2Subjective2023

Loading whiteboard...