Consider two gambles \(\tilde{x}_{1}=\{0,1 ; 0.3,0.7\}\) and \(\tilde{x}_{2}=\{0, x ; \pi, 1-\pi\}\), with \(x \in[0,1]\). Provide necessary and sufficient conditions on \(x\) and \(\pi\) so that

(i) \(\tilde{x}_{1} \succeq_{\text {FSD }} \tilde{x}_{2}\);

(ii) \(\tilde{x}_{1} \succeq_{\mathrm{SSD}} \tilde{x}_{2}\);

(iii) \(\tilde{x}_{1} \succeq_{\text {SSD }}^{M} \tilde{x}_{2}\);

(iv) \(\tilde{x}_{1} \succeq_{\mathrm{MV}} \tilde{x}_{2}\).