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out of total 150 students 45 passed in accounts , 50 passed in maths
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out of total 150 students 45 passed in accounts , 50 passed in maths R...
Sets, Functions and Relations:


Sets:



  • A set is a collection of distinct objects or elements.

  • The elements of a set can be anything like numbers, words, or even other sets.

  • Set theory is the branch of mathematics that deals with sets.



Functions:



  • A function is a relation between two sets where each element of the first set is related to exactly one element of the second set.

  • The set containing the first set's elements is called the domain, and the set containing the second set's elements is called the range.

  • A function can be represented using a graph, a table, or an equation.



Relations:



  • A relation is a set of ordered pairs where the first element of each pair is related to the second element.

  • A relation can be represented using a graph, a table, or a set of ordered pairs.

  • Relations can be classified as functions or non-functions.



Problem:



  • Out of a total of 150 students, 45 passed in accounts and 50 passed in math.

  • The number of students who passed in both subjects is unknown.



Solution:



  • Let A be the set of students who passed in accounts.

  • Let M be the set of students who passed in math.

  • The number of students who passed in both subjects can be represented by the intersection of the sets A and M.

  • Let B be the set of students who passed in both subjects.

  • B = A ∩ M

  • The number of students who passed in both subjects can be found by finding the cardinality of the set B.

  • |B| = 150 - (|A| + |M|)

  • |A| = 45

  • |M| = 50

  • |B| = 150 - (45 + 50) = 55

  • Therefore, 55 students passed in both accounts and math.

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out of total 150 students 45 passed in accounts , 50 passed in maths Related: Sets, Functions and Relations?
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