ધારો કે \(S =\{1,2,3, \ldots, 10\}\). ધારો કે \(S\) ના બધાજ ઉપગણોનો ગણ \(M\) છે. તો સંબંધ \(R =\{( A , B ): A \cap B \neq \phi\); \(A , B , \in M \}\) એ ........... છે.

A ફક્ત સંમિત અને સ્વવાચક
B ફક્ત સ્વવાચક
C ફક્ત સંમિત અને પરંપરિત
D ફક્ત સંમિત

Verified Solution

Answer & Solution

Correct Answer

(D) ફક્ત સંમિત

Step-by-step Solution

Detailed explanation

Let \(S=\{1,2,3, \ldots, 10\}\) \(R=\{(A, B): A \cap B \neq \phi ; A, B \in M\}\) For Reflexive, \(M\) is subset of ' \(S\) ' So \(\phi \in \mathrm{M}\) for \(\phi \cap \phi=\phi\) \(\Rightarrow\) but relation is \(\mathrm{A} \cap \mathrm{B} \neq \phi\) So it is not reflexive.…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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