Question

Find the cardinal number of the following sets.
(i) M = {p, q, r, s, t, u}
(ii) P = {x : x = 3n+2, n∈W and x< 15}
(iii) Q = {y : y = 3n4 , n ∈N and 2 < n ≤5}
(iv) R = {x : x is an integers, x∈Z and –5 ≤ x <5}
(v) S = The set of all leap years between 1882 and 1906.

Answer 1

1. Clearly n(M) = 6

2. P = { 2, 5 , 8, 11, 14 }
since P contains 5 elements n(P) = 5

3.Q = {243, 768, 1875 }
since Q contains 3 elements n(Q) = 3

4.R = { -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}
since R contains 10 elements n(R) = 10

5. S = { 1884, 1888, 1892, 1896, 1904}
since S contains 5 elements n(S) = 5

I hope this answer helps you

Answer 2

Cardinal number suggests the number of distinct elements in the set
So,
Ans 1)
There are 6 distinct elements in set so,
n(M)=6

Ans 2)
The elements of the set are 
P={2,5,8,11,14}
So there are 5 distinct elements so,
n(P)=5

Ans 3)

The elements of set are
Q={243,768,1875}
So, there are 3 distinct elements so,
n(Q)=3

Ans 4)
The elements of set are
R={-5,-4,-3,-2,-1,0,1,2,3,4}
So, there are 10 distinct elements so,
n(R)=10

Ans 5)
The elements of set are
S={1884,1888,1892,1896,1904}
So, there are 5 distinct elements so,
n(S)=5