In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. No picture is an album.
II. All albums are frames.
III. Some frames are portraits.
Conclusions:
I. No picture is a frame.
II. Some pictures are portraits.
- AOnly conclusion II follows
- BNeither conclusion I nor II follows
- CBoth conclusions I and II follow
- DOnly conclusion I follows
Solution & Step-by-step Explanation
Let's evaluate the statements via Venn diagrams:
Statement I: "No picture is an album." (Disjoint sets for Picture and Album)
Statement II: "All albums are frames." (The set of Album is completely inside the set of Frames)
Statement III: "Some frames are portraits." (Overlapping region between Frames and Portraits)
Now let's check the conclusions:
Conclusion I: "No picture is a frame." Since 'All albums are frames', some part of 'Frames' contains 'Albums'. We know 'No picture is an album', but 'Pictures' could still potentially overlap with the other outer part of 'Frames'. Thus, "No picture is a frame" is not universally true. It does not follow.
Conclusion II: "Some pictures are portraits." There is no stated relationship or restriction connecting 'Pictures' and 'Portraits' directly. They might overlap or might be completely separate. Thus, it doesn't definitely follow.
Since neither conclusion follows automatically under all conditions, the correct answer is "Neither conclusion I nor II follows".
Statement I: "No picture is an album." (Disjoint sets for Picture and Album)
Statement II: "All albums are frames." (The set of Album is completely inside the set of Frames)
Statement III: "Some frames are portraits." (Overlapping region between Frames and Portraits)
Now let's check the conclusions:
Conclusion I: "No picture is a frame." Since 'All albums are frames', some part of 'Frames' contains 'Albums'. We know 'No picture is an album', but 'Pictures' could still potentially overlap with the other outer part of 'Frames'. Thus, "No picture is a frame" is not universally true. It does not follow.
Conclusion II: "Some pictures are portraits." There is no stated relationship or restriction connecting 'Pictures' and 'Portraits' directly. They might overlap or might be completely separate. Thus, it doesn't definitely follow.
Since neither conclusion follows automatically under all conditions, the correct answer is "Neither conclusion I nor II follows".