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

Solution:

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;

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