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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements. Statements: Some tablets are laptops. All laptops are desktops. Conclusions: (I) Some desktops are tablets. (II) No desktops are tablets.
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Only conclusion (II) follows
Neither conclusion (I) nor (II) follows
Only conclusion (I) follows
Visualize Venn diagrams: Since all laptops are inside desktops and some tablets are laptops, the overlapping region of tablets and laptops must necessarily lie within the desktop circle.
Visualize Venn diagrams: Since all laptops are inside desktops and some tablets are laptops, the overlapping region of tablets and laptops must necessarily lie within the desktop circle.
Analyze Statement Relationships
From 'All laptops are desktops', we know the set of laptops is entirely contained within the set of desktops. From 'Some tablets are laptops', we know there is an intersection between tablets and laptops.
Deduce Logical Implication
Because the entire set of laptops is a subset of desktops, any tablet that is a laptop must also be a desktop. Therefore, the intersection of tablets and laptops is a subset of the intersection of tablets and desktops.
Evaluate Conclusions
Conclusion (I) 'Some desktops are tablets' is true because the laptops that are tablets are also desktops. Conclusion (II) 'No desktops are tablets' is explicitly contradicted by the fact that some desktops are indeed tablets.
A: Wrong because (II) is false; C: Wrong because (I) is true; D: Wrong because (I) follows.
B is correct because the deduction confirms that the overlapping region of tablets and laptops is contained within the 'desktops' category, making 'Some desktops are tablets' a valid inference.
Always look for the 'All' relationship first; if A is within B, any intersection with A necessarily forces an intersection with B.
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