Math 30-2 Chapter 1 Test Prep - Sets and Venn Diagrams

Flashcards covering core concepts from the notes: disjoint vs intersecting sets, universal and subset concepts, Venn diagram shadings, union/intersection/complement, cardinalities, and specific problem scenarios (hockey/soccer, reading genres, pizza problem).

Are sets C = { x | -5 ≤ x ≤ -1 } and D = { y | 1 ≤ y ≤ 5 } disjoint or intersecting? Explain using words or a diagram.

Disjoint; C contains negative numbers only and D contains positive numbers only, so there is no overlap.

What is sets

In U = { x | 1 ≤ x ≤ 50, x ∈ N }, P = { numbers that are perfect squares }, N = { numbers that are not perfect squares }, E = { even perfect square numbers }. Which diagram correctly represents these sets within U? Diagram

Diagram 1.

If Hockey has 75 students and Soccer has 60 students among the same Grade 12 class, with total Grade 12 students equal to 100, how many students are enrolled in both hockey and soccer?

35 students (use inclusion-exclusion: 100 = 75 + 60 − |H ∩ S|).

What does A ∪ B represent in a Venn diagram?

All elements that are in A or in B or in both.

What does A ∩ B represent?

Elements common to both A and B.

What is the complement of A (A') with respect to a universal set U?

All elements in U that are not in A.

What does n(U) denote?

The number of elements in the universal set U.

What is n(A ∪ B) in terms of n(A), n(B), and n(A ∩ B)?

n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

What is n(B \ A)?

n(B) − n(A ∩ B).

If |Fiction| = 150 and |Non-fiction| = 70 in a survey of 200 people, what is the minimum possible number who read both?

20 (minimum intersection = 150 + 70 − 200).

In the same scenario, what is the maximum possible number who read both?

70 (limited by the smaller set).

Statement: J ∩ L = ∅. True or false?

True; this means J and L are disjoint sets.

If J ⊂ M, what does this indicate about J and M?

Every element of J is also an element of M.

What does B \ A denote in set notation?

Elements that are in B but not in A.

A common error when interpreting Venn diagrams is misplacing numbers in the wrong region. How can you avoid this error?

Carefully assign counts to each region using inclusion-exclusion and verify totals; double-check overlaps are counted correctly.

Pizza, Sandwich, and Burger problem: How many people were surveyed?

200.

Pizza, Sandwich, and Burger problem: How many people liked at least one of the three foods?

180.

Pizza, Sandwich, and Burger problem: How many people liked all three foods?

28.

Fill in the region counts for the three-food Venn diagram: Pizza only, Sandwich only, Burger only, Pizza∩Sandwich only, Sandwich∩Burger only, Pizza∩Burger only, All three, None.

Pizza only = 18; Sandwich only = 7; Burger only = 32; Pizza∩Sandwich only = 35; Sandwich∩Burger only = 18; Pizza∩Burger only = 42; All three = 28; None = 20.

Which word has more distinct letters, MATHEMATICS or CASH? How many distinct letters does each have?

MATHEMATICS has 8 distinct letters (M, A, T, H, E, I, C, S); CASH has 4 distinct letters (C, A, S, H).