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Option 4 : Neither I nor III follows

Consider the following least possible Venn diagram,

[ alt="SSC Steno FT6 Neha 50q Hindi reviewed images Q30" src="//storage.googleapis.com/tb-img/production/18/07/SSC_Steno_FT6_%20Neha%20_50q_Hindi%20reviewed_images_Q30.PNG" style="height:144px; width:274px">

Conclusions:

I. No Bed is a Pen → False (It is possible but not definite).

II. Some Woods are Cycles → True.

III. Some Pens are Woods → False (It is possible but not definite).

Hence, neither conclusion I nor III follows.
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