सिद्ध कीजिए कि \( \mathrm{A}=\{1,2,3,4,5\} \) में, \( \mathrm{R}=\{...

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सिद्ध कीजिए कि \( \mathrm{A}=\{1,2,3,4,5\} \) में, \( \mathrm{R}=\{(a, b):|a-b| \) सम है \( \} \) द्वारा प्रदत्त संबंध \( \mathrm{R} \) एक तुल्यता संबंध है। प्रमाणित कीजिए कि \( \{1,3,5\} \) के सभी अवयव एक दूसरे से संबंधित हैं और समुच्चय \( \{2,4\} \) के सभी अवयव एक दूसरे से संबंधित हैं परंतु \( \{1,3,5\} \) का कोई भी अवयव \( \{2,4\} \) के किसी अवयव से संबंधित नहीं है।
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