Question

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

Answer 1

Consider the set A and set B;

`A=\mleft\lbrace x\in N\colon P(x\mright)\},B=\mleft\lbrace x\in N\colon O(x)\mright\rbrace`

Let P be the property "is a prime number" and O be the property "is an odd integer".

`\begin{gathered} A=\mleft\lbrace2,3,5,7,11,\ldots\mright\rbrace,B=\mleft\lbrace1,3,5,7,9,11,\ldots\mright\rbrace \\ A\text{ is not a subset of set B} \end{gathered}`

Also;