Q. 3

• What is a pyramid in geometry?

  A three-dimensional geometric shape
• What is the base of a pyramid?

  A polygon where triangular sides meet
• What is the apex of a pyramid?

  The top point where triangles meet
• What is the height of a pyramid?

  The perpendicular distance from apex to base
• What is the slant height of a pyramid?

  The distance along a lateral face
• What defines a set in mathematics?

  A collection of well-defined, distinct objects
• What are the objects in a set called?

  Elements
• What is a subset?

  A set whose elements are in another set
• What is set notation used for?

  To list numbers, objects, or outcomes
• What symbols are used in set notation?

  Curly brackets { }
• What is a finite set?

  A set with a limited number of elements
• What is an infinite set?

  A set with unlimited elements
• What is an empty or null set?

  A set with no elements
• What is a universal set?

  A set containing all relevant elements
• UNION OF SET (∪) - A ∪ B is the set that contains all the elements in either A or B. INTERSECTION (∩) - A ∩ B is the set that contains all common elements between sets A and B. EXAMPLE 1 Let M = {B, E, A, U, T, O} and N = {F, O, B, A, I, N} What is M ∪ N? Solution: Since the operation is union of sets, we have to combine all the letters but write the repeated letters only once. Thus M ∪ N = {B, E, A, U, T, O, F, I, N} To find the intersection, just enumerate the common elements of M and N. So, we have M ∩ N = {B, A}
• A. FINITE SET - The set has a limited number of elements and can be counted. B. INFINITE SET - The set has an unlimited number of elements, which may or may not be countable. C. EMPTY OR NULL SET The set has no elements. D. UNIVERSAL SET The set contains all relevant elements for a particular context. THE FOLLOWING ARE EXAMPLES OF EACH TYPE OF SET EXAMPLE OF FINITE SETS: The set of planets in the solar system. S = {5, 10, 15, 20, 25}
• VENN DIAGRAM A VENN DIAGRAM is used to represent relationships between a collection of objects or sets. • As shown below, a rectangle with circles inside represents the universal set. • VENN DIAGRAM usually represents the different subsets in the universal set. The letter names of the universal set is written beside it. A = {1, 2, 3} B = {3, 4, 5} U = {1, 2, 3, 4, 5, 6} A ∪ B = {1, 2, 3, 4, 5} A ∩ B = {3}
• Let O = {positive odd numbers} and E = {positive even numbers} What is the union of sets O and E? Solution: If we combine the sets O and E, their union would be the set of counting numbers or, in set notation, O ∪ E = {1, 2, 3, 4, 5, ...} Their intersection is an empty set, that is O ∩ E = {}