Question

please solve the problem and help​

Answer 1

Step-by-step explanation:

Given the universal set : -

U = { x : x ∈ N , 11 < x < 25 }

∵ x ∈ N ( x belongs to natural number), the given set in the roaster form will be,

↬ U = { 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 }

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Given set A : -

A = { x : x > 19 }

∵ A is a subset of U, set A can be written in the roaster form as,

↬ A = { 20 , 21 , 22 , 23 , 24 } -----Eqⁿ(1)

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Given set B : -

B = { x : x ≤ 18 }

∵ B is also a subset of U, the set B in the roaster form can be expressed as,

↬ B = { 12 , 13 , 14 , 15 , 16 , 17 , 18 } -----Eqⁿ(2)

Cardinal number is the number of elements present in the set.

From equation 1 and 2 :-

↪ Cardinal number of set A = 5

↪ Cardinal number of set B = 7

More :-

A set can be written in 3 different forms - set builder form, roaster form and visual representation.

• In set builder form, we write common properties of all the elements of the set.

• In roaster form, we write all the elements of set instead of their common properties.

• In visual representation, we represent the set by using Venn diagrams.

There are some symbols to represent the sets.

• Set of all the natural numbers is donated by N.

• Set of all whole numbers is donated by W.

• Set of all real numbers is donated by R.

• Set of all irrational number is donated by T.

• Set of all rational numbers is donated by Q.

• Set of complex numbers is donated by C.

Cardinal number is the number of total elements present in the given set. Can also be written as n(K) for some set K.

There are some symbols associated with the set theory.

• ∩ - Intersection

• ∪ - Union

• A' - Compliment for some set A

• ϕ - phi or empty set

• ∈ - Belongs to

• ∀ - For all