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Given the following set, select the statement below that is true.
\n" ); document.write( "A = {q, r, s, t, u}
\n" ); document.write( "
\n" ); document.write( " p ∈ A
\n" ); document.write( " 5 ∈ A
\n" ); document.write( " r ∉ A
\n" ); document.write( " s ∈ A
\n" ); document.write( " A Ø\r
\n" ); document.write( "\n" ); document.write( "∈ means that something is an element or member of a set. For example, if C = {1, 3, 5, 7}, 3 is within set C, so 3 ∈ C
\n" ); document.write( "Therefore, see my reasoning for each possible answer.\r
\n" ); document.write( "\n" ); document.write( "==> p ∈ A
\n" ); document.write( "This is saying that p is part of set A. However, when you look at the elements of A (A = {q, r, s, t, u}, so the elements of a are q, r, s, t, and u), there is no p, so this is FALSE, and the incorrect answer.
\n" ); document.write( "==> 5 ∈ A
\n" ); document.write( "This is saying that 5 is part of set A. However, as said previously, the only elements of A are q, r, s, t, and u--there is no 5 among these. Therefore, this is FALSE, and the incorrect answer.
\n" ); document.write( "==> r ∉ A
\n" ); document.write( "This is saying that r is an element of set A. However, when you look at the elements of set A (q, r, s, t, and u), there IS an r, so this is FALSE, and the incorrect answer.
\n" ); document.write( "==> s ∈ A
\n" ); document.write( "This is saying that s is an element of set A. When you look at the elements of set A (q, r, s, t, and u), s IS included, so this is TRUE, and the correct answer.
\n" ); document.write( "==> A Ø
\n" ); document.write( "This is saying that there are no elements in set A. However, it says before that that A encompasses q, r, s, t, and u, so it must have elements--they are stated right there! Therefore, this is FALSE, and the incorrect answer.\r
\n" ); document.write( "\n" ); document.write( "***Therefore, the correct answer is that s ∈ A \n" ); document.write( "