how many elements are there in the following sets
a) the set of all solutions of the quadric equation x^2 = 25
b) the set of squares of all natural numbers
Answers
Step-by-step explanation:
The number of elements in the following sets :
(i) The set of all solutions of the quadratic equation
\sf{ {x}^{2} = 25 }x
2
=25
(ii) The set of squares of all natural numbers.
CONCEPT TO BE IMPLEMENTED
SET : A set is a well defined collection of distinct objects
Finite Set : A set is said to be finite set if the set contains finite number of elements
Infinite Set : A set is said to be infinite set if the set contains infinite number of elements
EVALUATION :-
(i) Here the given Quadratic Equation is
\sf{ {x}^{2} = 25}x
2
=25
\sf{ \implies x \: = \: \pm \: 5}⟹x=±5
Hence the set of all solutions of the quadratic equation is = { - 5, 5 }
Hence the number of elements in the set = 2
(ii) Here the set of natural numbers is
\mathbb{N} = \{ 1,2,3,4,....... \}N={1,2,3,4,.......}
So the set of squares of all natural numbers
= { 1,4,9,16,.......}
So the set contains infinite number of elements
Hence the number of elements in the set is infinite
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