Clarify wording and change correct answer for TF statements

OpenProblemLibrary/WHFreeman/Holt_linear_algebra/Chaps_1-4/4.2.41_47a.pg

@@ -62,24 +62,19 @@ $tf->rf_print_q(~~&pop_up_list_print_q);
 $tf->ra_pop_up_list( 
 [ No_answer => "?", "T"=>"True", "F"=>"False"] ); 
 
-#$a = random(2,3,1);
-#$aa = $a+1;
-#$b = random(6,9,1);
-#$c = random(7,10,1);
-
 # Questions and answers
 $tf -> qa ( 
 "If  \(\  S_1  \)  and \(\  S_2  \) are subspaces of \( R^n\) of the same dimension, then \(S_1=S_2\).",
 "F",
 "If  \( \  S =\) span{\(u_1, u_2, u_3 \)},  then  \(dim(S) = 3\) .",
 "F",
-"If the set of vectors \(U\) spans a subspace \(S\), then vectors can be added to \(U\) to create a basis for \(S\)",
-"F",
-"If the set of vectors \(U\) is linearly independent in a subspace \( S\) then vectors can be added to \(U\) to create a basis for \(S\)",
-"F",
-"If the set of vectors \(U\) spans a subspace \(S\), then vectors can be removed from \(U\) to create a basis for \(S\)",
+"If the set of vectors \(U\) spans a subspace \(S\), then vectors can be added to \(U\) to create a basis for \(S\) (i.e. there is a set of vectors \(V\) with \(U\subseteq V\) which is a basis of \(S\)).",
 "F",
-"If the set of vectors \(U\) is linearly independent in a subspace \( S\) then vectors can be removed from \(U\) to create a basis for \(S\).",
+"If the set of vectors \(U\) is linearly independent in a subspace \( S\) then vectors can be added to \(U\) to create a basis for \(S\) (i.e. there is a set of vectors \(V\) with \(U\subseteq V\) which is a basis of \(S\)).",
+"T",
+"If the set of vectors \(U\) spans a subspace \(S\), then vectors can be removed from \(U\) to create a basis for \(S\) (i.e. there is a set of vectors \(V\) with \(V\subseteq U\) which is a basis of \(S\)).",
+"T",
+"If the set of vectors \(U\) is linearly independent in a subspace \( S\) then vectors can be removed from \(U\) to create a basis for \(S\) (i.e. there is a set of vectors \(V\) with \(V\subseteq U\) which is a basis of \(S\)).",
 "F",
 "Three nonzero vectors that lie in a plane in \(R^3\) might form a basis for \(R^3\).",
 "F",