Read the given statements and conclusions carefully. Assuming that the…

In categorical syllogisms, a term is distributed only when a statement makes a claim about every member of that class. A universal statement (All A are B) distributes its subject; a particular statement (Some A are B) distributes neither term. A definite conclusion linking two end terms through a shared middle term generally needs that middle term to be distributed in at least one premise -- when the only premises connecting two terms are both particular ("Some"), no definite overlap between those two terms can be forced, because more than one diagram remains compatible with the premises.

1. Symbolise the statements: All mirrors (M) are houses (H), so M sits fully inside H. Some kites (K) are houses (H), so K and H share at least one point. Some figs (F) are kites (K), so F and K share at least one point.

2. Test "Some houses are figs": houses and figs are connected only through kites, and both the kite-house link and the kite-fig link are particular. Draw the fig portion of kites entirely in the part of K that lies outside H -- every statement still holds (M inside H, K meeting H, F meeting K), but H and F now share no point, so this overlap is not forced.

3. Test "Some kites are mirrors": mirrors are only known to sit inside houses, and houses can extend well beyond the mirror region, so the kite-house overlap can be drawn entirely in the part of H that lies outside M -- every statement still holds, but K and M now share no point, so this overlap is not forced either.

The diagram built for conclusion (I) directly falsifies it by placing the fig portion of kites outside houses -- this reflects that kites, the middle term linking houses and figs, is undistributed in both relevant premises (both are particular). The diagram built for conclusion (II) directly falsifies it by placing the kite-house overlap outside mirrors -- here houses is the middle term linking mirrors and kites, and houses is undistributed in both relevant premises too (the universal premise distributes only mirrors, and the particular premise distributes neither term). Each diagram is an independent countermodel for its own conclusion, so neither overlap is forced by the given statements. Hence neither conclusion (I) nor (II) follows.