Equivalence classes: even and odd integersतुल्यता वर्ग: सम और विषम पूर्णांकEquivalence classes: even aur odd integers

NCERT Example 5 · Class 12 Maths · Chapter 1 · interactive diagram

Parts and what they mean

• Set of integers Z (पूर्णांकों का समुच्चय Z) — The whole set on which R is defined.
• Class of even integers E = [0] (सम पूर्णांकों का वर्ग E = [0]) — All even numbers are related to each other (their difference is even) and to 0.
• Class of odd integers O = [1] (विषम पूर्णांकों का वर्ग O = [1]) — All odd numbers are related to each other and to 1.
• Disjoint, and together they make Z (असंयुक्त, और मिलकर Z बनाते हैं) — No even number is related to an odd number; every integer is in exactly one class.
• The relation R (संबंध R) — a R b when a − b is divisible by 2. R is an equivalence relation.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 5. Report a mistake