Math Problem Statement

A set of mathematical problems involving set theory, probability, and relations. Problems include finding intersections of sets, transitive closure of relations, and computing probabilities from dice rolls and card draws.

Solution

This image contains a set of mathematical and logical questions. Let me break it down into its parts and provide a brief overview of the problems:

  1. Set Theory & Relations: There is a problem dealing with finding how many people like singing and dancing, given set relationships. You're asked to express sets like AA and BB, and then calculate intersections and unions.

  2. Transitive Closure: You are asked to find the transitive closure of a given relation.

  3. Probability: There is a question asking for the probability of drawing certain cards from a deck, as well as questions related to functions and rules defined by equations.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Relations
Probability
Functions

Formulas

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
P(E) = (Favorable Outcomes) / (Total Outcomes)
Transitive Closure of a Relation

Theorems

Basic Set Identities
Probability Rules
Transitive Closure Theorem

Suitable Grade Level

Grade 10-12

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