MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Cardinality

Find the card...

Question

Find the cardinal number of the following sets
(i) $A =$ ${$ $x : x = 5^{n}, n \in N$ and $n < 5$ $}$
(ii) $B =$ ${$ $x : x$ is a consonant in English Alphabet $}$
(iii) $X =$ ${$ $x : x$ is an prime number $}$
(iv) $P = {x : x < 0, x \in W}$
(v) $Q = {x : - 3 \leq x \leq 5, x \in Z}$

Open in App

Solution

Number of element in a set is called cardinal number.
$(1) A = {5, 25, 125, 625}$
$n (A) = 4$
$(2) B = {b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, u, v, w, x, y, z}$
$n (B) = 21$
$(3) X = {2, 3, 5, 7, 11......}$
$n (x) = i n f i n i t e$
$(4) Q = {- 3, - 2, - 1, 0, 1, 2, 3, 4, 5}$
$n (A) = 9$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Which of the following sets are equivalent?
(i)

A = {2, 4, 6, 8, 10}, B = {1, 3, 5, 7, 9}

X = {x : x \in N, 1 < x < 6}, Y =

x : x

is a vowel in the English Alphabet }
(iii)

P =

{

x : x

is a prime number and

5 < x < 23

}

Q = {x : x \in W, 1 < x < 5}

Q. Write the following sets in Roster form
(i)

A = {x : x \in N, 2 < X \leq 10}

B = {x : x \in Z, - \frac{1}{2} < X < \frac{11}{2}}

C =

x : x

is a prime number and a divisor of 6 }
(iv)

X =

x : x = 2^{n}, n \in N

n \leq 5

M = {x : x = 2 y - 1, y \leq 5, y \in W}

P =

x : x

x^{2} \leq 16

Q. Find the cardinal number of the following sets.
(i)

A =

x : x

is a prime factor of 12 }
(ii)

B = {x : x \in W, x \leq 5}

Q. Taking the set of natural numbers as the universal set, write down the complements of the following set:

(i) {x : x

is an even natural number

}

(i i) {x : x

is an odd narutal number

}

(i i i) {x : x

is a positive multiple of

3}

(i v) {x : x is a prime number}

(v) {x : x is a natural number divisible by 3 and 5}

(v i) {x : x is a perfect square}

(v i i) {x : x is a perfect cube}

(v i i i) {x : x + 5 = 8}

(i x) {x : 2 x + 5 = 9}

(x) {x : x \geq 7}

(x i) {x : x \in N and 2 x + 1 > 10}

A \cup B

A \cap B

for the following sets.
(i)

A = {0, 1, 2, 4, 6}

B = {- 3, - 1, 0, 2, 4, 5}

A = {2, 4, 6, 8}

B = \emptyset

A = {x : x \in N, x \leq 5}

B =

x : x

is a prime number less than 11}
(iv)

A = {x : x \in N, 2 < x \leq 7}

B = {x : x \in W, 0 \leq x \leq 6}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Sets and Their Representations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard VI Mathematics

Join BYJU'S Learning Program

CrossIcon