Question

Let a set E ={0,2,4,6,8... } of non-negative even numbers and O = {1, 3, 5, 7, 9,...} of non-negative odd numbers then a) Cardinality of set E is greater thanthat of O b) Cardinality of set O is greater than that of E c) Cardinality of set E is equal to that of o d) None of the mentioned

Answer 1

Answer:

C. Cardinality of set E is equal to that of O

Step-by-step explanation:

We are given that two sets

a set E of non negative even numbers

E={0,2,4,....}

A set O of non negative odd numbers

O={1,3,5,.....}

We have to choose correct option in given options

We know that

Set of non negative even numbers is countably infinite and set of non negative odd numbers is also countably infinite.

Cardinality of countably infinite set=Aleph naught=$\chi_0$

Therefore, cardinality of E=$\chi_0$

Cardinality of O=$\chi_0$

Therefore, the cardinality of set  E is equal to cardinality of set O.

Hence, option C is true.