समुच्चय \(A =\{ a , b , c \}\) पर निम्न दो द्विआधारी संबंधों पर विचार कीजिए \(R _{1}=\{( c , a ),( b , b ),( a , c ),( c , c ),( b , c ),( a , a )\}\) और \(R _{2}=\{( a , b ),( b , a ),( c , c ),( c , a ),( a , a ),( b , b ),( a , c )\}\) तो

A \(R _{2}\) सममित नहीं है परन्तु संक्रामक है।
B \(R _{1}\) तथा \(R _{2}\) दोनों सममित नहीं हैं।
C \(R _{1}\) तथा \(R _{2}\) दोनों संक्रामक नहीं हैं।
D \(R _{1}\) सममित है परन्तु संक्रामक नहीं है।

Verified Solution

Answer & Solution

Correct Answer

(A) \(R _{2}\) सममित नहीं है परन्तु संक्रामक है।

Step-by-step Solution

Detailed explanation

both \({R_1}\) and \({R_2}\) are symmetric as For any \(\left( {x,y} \right) \in {R_1}\), we have \(\left( {y,x} \right) \in {R_1}\) and similarly for \({R_2}\) Now, for \({R_2},\left( {b,a} \right) \in {R_2},\left( {a,c} \right) \in {R_2}\) but…

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.

Same subject

Explore more questions on app

From JEE Mains

Explore more questions on app