📘 set theory

1. **State the problem:** We are given the sizes of sets and their union and need to find the size of the intersection of sets A and B. 2. **Given:**

1. **State the problem:** We surveyed 750 students about tattoos and body piercings. Given:

1. **State the problem:** We are given three sets of states: $$K = \{DE, FL, NJ, NY, PA\}$$

1. **State the problem:** We are given the number of people who own a cat but not a dog, own a dog but not a cat, and the total number of people who own a cat or a dog (or both). W

1. The problem involves finding intersections and unions of sets P, Q, X, and Y based on the Venn diagram values. 2. Recall the definitions:

1. **Problem statement:** We have 50 students, each speaks at least one language: English (E), French (F), or German (G). Given: $|E|=30$, $|F|=15$, $|G|=19$, $|E \cap G|=6$, $|E \

1. **State the problem:** We have a Venn diagram showing guests who had ice cream, custard, both, or neither at a wedding. The numbers are: - Ice Cream only: 51

1. **State the problem:** We have 80 students in total.

1. **Stating the problem:** We have a survey about preferences for Newari food (set $N$) and Thakali food (set $T$). Given: 70% like Newari food, 60% like Thakali food, 20% like ne

1. **Problem:** Prove that the relation $R$ on $\mathbb{R} \times \mathbb{R}$ defined by $(a,b) R (x,y)$ iff $a \leq x$ and $b \leq y$ is a partial ordering. 2. **Recall:** A relat

1. **State the problem:** We have a group of students where 30 play cricket, 38 play football, and 9 play neither cricket nor football. We need to find the lowest possible number o

1. Exercise 1: Determine truth of assertions for set $A = \{1,2,3\}$. - $3 \in A$: True, since 3 is an element of $A$.

1. **State the problem:** We are given a Venn diagram showing how many Key Club members watch Tennis, Football, and Baseball on television. We need to determine which statements ab

1. **State the problem:** Find the union of sets A and B, where Set A = factors of 12, Set B = factors of 10.

1. **Problem:** Shade the region of the Venn Diagram indicated by the set expression $(A' \cup B) \cap C$. 2. **Understanding the notation:**

1. **Problem:** List the elements of the set $\{ x : x \in \mathbb{N}, 5 < x < 12 \}$ where $\mathbb{N} = \{1, 2, 3, \ldots\}$. 2. **Understanding the problem:** We want all natura

1. **List the elements of the sets:** **a)** $\{ x : x \in \mathbb{N}, 5 < x < 12 \}$ means natural numbers greater than 5 and less than 12.

1. The problem involves shading regions in Venn diagrams for sets A and B. 2. For part a, we need to shade set B. This means shading all elements that belong to B, including the in

1. **Problem statement:** We are given sets of months and need to find the cardinalities of certain unions, intersections, and complements. 2. **Recall the universal set and subset

1. **Problem statement:** Re-examine the calculations for $n(J \cap V)$ and $n(R')$ given the sets defined over the months of the year. 2. **Step 1: Recall the sets:**

1. **Problem statement:** Given the universal set $U$ as the months of the year, and sets $J$, $Y$, $V$, and $R$ defined by certain letter conditions, find: - $n(J \cup Y)$