Example 4: reflexive, but not symmetric, not transitiveउदाहरण 4: स्वतुल्य, पर सममित नहीं, संक्रामक नहींExample 4: reflexive, par symmetric nahi, transitive nahi

NCERT Example 4 · Class 12 Maths · Chapter 1 · interactive diagram

Parts and what they mean

• (1, 1), (2, 2), (3, 3) — every element related to itself ((1, 1), (2, 2), (3, 3) — हर अवयव स्वयं से संबंधित) — All three pairs (a, a) are in R, so R is reflexive.
• (1, 2) ∈ R ((1, 2) ∈ R) — (1, 2) is in R but (2, 1) is not, so R is NOT symmetric.
• (2, 3) ∈ R ((2, 3) ∈ R) — With (1, 2) this would need (1, 3) for transitivity.
• (1, 3) is missing ((1, 3) नहीं है) — (1, 2) ∈ R and (2, 3) ∈ R but (1, 3) ∉ R, so R is NOT transitive.
• Set A = {1, 2, 3} (समुच्चय A = {1, 2, 3}) — A relation in A is a subset of A × A: arrows start and end in A.
• Set A again (वही समुच्चय A) — A is drawn twice only to show the arrows clearly.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 4. Report a mistake