4) show that the cardinality of the negative even numbers is the same as all of the odd numbers

Answer with Step-by-step explanation:

We are given that two sets one set consist of negative even numbers and other set consist of all  odd numbers.

We have to show that Cardinality of negative even number is same as cardinality of set of all odd numbers.

Suppose set A={-2,-4,-6,...}

B={...,-3,-1,1,3,5,...}

Set A is countably infinite set and set B is also countably infinite set .

We know that all countably infinite set have same cardinality .

Therefore,Set A  and set B have same cardinality.