Slice selection gradient
CORRECT. The slice thickness is governed by the following equation:
thk = BWtrans / (ω0·GS)
where thk is the slice thickness, BWtrans is the transmitted RF bandwidth (the range of frequencies it covers), γ0 is the gyromagnetic ratio and GS is the magnitude of the slice selection magnetic field gradient.
So, slice thickness is inversely proportional to GS; increasing GS will yield a thinner imaging slice.

Slice selection method
INCORRECT. Increasing the slice-selection gradient magnitude means (for the duration of the gradient field) a larger range of Larmor frequencies exists along the patient.
Before a gradient increase, the RF excitation pulse bandwidth excited a particlar range of frequencies (which corresponded to a particular image slice). If the slice-selection gradient is increased, to what does the same range of frequencies correspond now?
Try again.
INCORRECT. A change of the slice-selection gradient magnitude cannot effect a change of slice location.
Try again.
Further reading on this topic:
Books: MRI From Picture to Proton p116, Q&A in MRI p75, MRI The Basics p100
Online: Medcyclopaedia, Basics of MRI