Chapter 4.5, Problem 80E

True or False? In Exercises $79$ and $80$, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows that the statement is not true in all cases or cite an appropriate statement from the text.

(a) If $\dim \left(V\right)=n$, then any set of $n+1$ vectors in $V$ must be linearly dependent.

(b) If $\dim \left(V\right)=n$, then any set of $n-1$ vectors in $V$ must be linearly independent.