Find the cardinal number of the following sets - iA1- -2- -1-1-3-5 iiA2- x-x -N-and-3- x - 7 iiiA3- p-p - W- and- 2p - 3-8 ivA4- b-b - Z -and-7-3b-1- 2 Cardinal-Number-of-set-The number of elements in a set is called its Cardinal Number-

(i)A_1={ 2, 1,1,3,5 } Cardinal number of set A_1= 5 Ans. (ii)A_2={ x:x ∈ N and 3 ≤ x lt; 7 } ={ 3,4,5,6 } ∴Cardinal number of set A_2= 4 Ans. (iii)A_3={ p: ...

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Standard VIII

Mathematics

Cardinality of Sets

Find the card...

Question

Find the cardinal number of the following sets :

(i) $A_{1} = {- 2, - 1, 1, 3, 5}$

(ii) $A_{2} = {x : x \in N a n d 3 \leq x < 7}$

(iii) $A_{3} = {p : p \in W a n d 2 p - 3 < 8}$

(iv) $A_{4} = {b : b \in Z a n d - 7 < 3 b - 1 \leq 2}$ $Cardinal~Number~of~set~:The number of elements in a set is called its Cardinal Number.$

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Solution

(i) $A_{1} = {- 2, - 1, 1, 3, 5}$ Cardinal number of set $A_{1} = 5$ Ans.

(ii) $A_{2} = {x : x \in N a n d 3 \leq x < 7}$ = ${3, 4, 5, 6}$ $∴$ Cardinal number of set $A_{2} = 4$ Ans.

(iii) $A_{3} = {p : p \in W a n d 2 p - 3 < 8}$

2P-3<8

$\Rightarrow 2 P < 11 \Rightarrow P < \frac{11}{2} (D i v i d i n g b o t h s i d e s b y 2) \Rightarrow P < 5.5 ∴ A_{3} = {0, 1, 2, 3, 4, 5} ∴ C a r d i n a l N u m b e r o f s e t A_{3} = 6 A n s .$

(iv) $A_{4} = {b : b \in Z a n d - 7 < 3 b - 1 \leq 2}$

-7<3b-1

$\Rightarrow - 7 + 1 < 3 b - 1 + 1 (A d d i n g 1 t o b o t h s i d e s) \Rightarrow - 6 < 3 b \Rightarrow - \frac{6}{3}$

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Find the cardinal number of the following sets : (i)A1={−2,−1,1,3,5} (ii)A2={x:x∈ N and 3 ≤x<7} (iii)A3={p:p ∈ W and 2p−3 < 8} (iv)A4={b:b∈Z and −7< 3b−1 ≤2} Cardinal~Number~of~set~:The number of elements in a set is called its Cardinal Number.