V is a nonzero finite-dimensional vector space, and the vectors listed belong to V. Mark each statement True or False. Justify each answer. a. If there exists a set \left\{\mathbf{v}_{1}, \dots, \mathbf{v}_{p}\right\}{v 1 ,…,v p } that spans V, then dim V \leq pV≤p. b. If there exists a linearly independent set \left\{\mathbf{v}_{1}, \dots, \mathbf{v}_{p}\right\}{v 1 ,…,v p } in V, then dim V \geq pV≥p. c. If dim V=p, then there exists a spanning set of p+1 vectors in V. Note:complex mathematical expressions, unable to write in this sheet