Discrete math 2.8. Let P be the property “is a prime number” and O be the proper

Question

Discrete math

2.8. Let P be the property “is a prime number” and O be the property “is an odd

integer.” Consider the sets A = {x N : P(x)} and B = {x N : O(x)}.
1. Examine A and B with respect to the subset relation. What can you conclude? Justify your

answer.
2. Are A and B equal? Justify your answer.

Modern notation for A S is A S, and we say that A is a subset of S. Thus,

ASif,andonlyif,forallx, ifxA, thenxS. When A is not a subset of S, we write A S.

Exercise 2.3. Describe what it means for A S that is similar to the description of A S given above.

Dedekind goes on to show that the subset relation satisfies the following properties.

Explanation / Answer

Solution:

A is the set of all prime numbers and B is the set of all odd numbers.

A = {2, 3, 5, 7....}

B={3, 5, 7, 9,....}

From this we can conclude that i) A is not subset of B and ii) B is not subset of A

1. Neither of the set is subset of other. A could be subset of B but 2 is prime but not odd. Hence A is not subset of B. Also, B contains all odd numbers which may or may not be prime. Hence B is not subset of A

2. A and B are not equal. Because there are all the numbers in A are not present in set B.

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