📘 set theory

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:

1. The problem asks for the number of pizzas that have chillies on them based on the Venn diagram. 2. According to the Venn diagram, the pizzas that have chillies are the ones insi

1. First, solve the arithmetic expression given: 3 \times 16 \div 3 = ? and 24 \times 8 + ? \div 2. Step 1: Calculate 3 \times 16 = 48.