📘 set theory

1. The problem: Given two sets \( A = \{2,4,6,8,10\} \) and \( B = \{1,3,5,7,9\} \), find a universal set that contains both sets.\n\n2. A universal set is a set that contains all

1. **Problem:** Find the complement of the intersection of sets A and B, i.e., $(A \cap B)'$. Given: - $A = \{1, 2, 3, 5\}$

1. Problem Statement: We have 22 pupils taking at least one of chemistry, economic, and government. Given: Economic (E) = 12, Government (G) = 6, Chemistry (C) = 7, Economic and Ch

1. **State the problem:** Find the total number of students who study Music (M). The numbers inside the Music circle are: 5 (only M), 3 (M and D), 4 (M and G), and 2 (M, D and G).

1. The problem asks for the complement of set B relative to set A, written as $B \mid A$ or $A \setminus B$, meaning all elements in $A$ that are not in $B$. 2. First, find the ele

1. **State the problem:** We have a squash club with 27 members. - 19 members have black hair.

1. The problem asks to calculate $n(P \cup Q' \cap R)$, where $P, Q, R$ are sets in a Venn diagram. 2. Identify the numbers given in the Venn diagram regions:

1. **State the problem:** We have 50 children choosing from beans, plantain, and rice.

1. **Stating the problem:** Given universal set $U = \{a, b, c, d, e, f, g\}$ and sets:

1. **State the problem:** Given the universal set $U = \{a, b, c, d, e, f, g\}$ and sets $A = \{a, b, c, d, e\}$, $B = \{a, c, e, g\}$, $C = \{b, d, f, g\}$, find the following: 2.

1. Problem statement: In a survey students were asked if they take demography D, sociology S, and psychology P with counts $n(S)=73$, $n(D)=51$, $n(P)=27$, $n(S∩D)=33$, $n(S∩P)=5$,

1. State the problem. We are given that 73 students take Sociology, 51 take Demography, 27 take Psychology, 2 take none of the three, 33 take Sociology and Demography, 18 take only

1. Stating the problem: We have three groups of students playing chess, scrabble, and draft with overlapping memberships. We need to find: (a) Number of students who play both ches

1. The problem is to evaluate the empty set notation \( \left\{\;\right\} \), which represents the set with no elements. 2. By definition, an empty set contains no members; it is u

1. The problem is about understanding the sets \(A\) and \(B\).\n\n2. Set \(A = \{x: x \text{ is an odd natural number}\}\) includes all positive integers that are odd, such as 1,

1. **State the problem:** Given the set $$A = \{ \{-2, 2\}, \{-1, 1\}, 0 \}\), determine which of the following subset statements are true. 2. **Analyze Choice A:** $$\{ -2, 2 \} \

**Problem statement:** We are given a function $f: E \to F$, two subsets $A, B$ and subsets $A_1, A_2 \subseteq E$, $B_1, B_2 \subseteq F$. We need to prove:

1. **Show that if $A_1 \subset A_2$, then $f(A_1) \subset f(A_2)$:** By definition, $f(A) = \{y \in F \mid \exists x \in A, f(x) = y\}$. If $A_1 \subset A_2$, then every element $x

1. **State the problem:** Show using a Venn diagram and set theory that if $A \subset B$ then $B' \subset A'$, and conversely, if $B' \subset A'$ then $A \subset B$.

1. **State the problem:** We want to show through a Venn diagram and logical reasoning that if $A \subset B$ then $B' \subset A'$, and conversely, if $B' \subset A'$, then $A \subs

1. The problem states that 30 people were surveyed about playing badminton and cricket, with a Venn diagram representing the counts. 2. The Venn diagram numbers are: