This category covers the fundamentals of set theory, including definitions, operations, and Venn diagrams. It also introduces relations, their properties, and how they connect elements of different sets. Functions are explained through mappings, domain, codomain, and types such as injective and surjective. Ideal for building a solid foundation in discrete mathematics.
Notice that after simplifying, Symmetric relation is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
The trick is we verify a – b = c – d by full calculation: use standard identity, substitute, simplify step by step to reach a – b = c – d.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Notice that we verify x² + y² + x + 2y = 0 by full calculation: use standard identity, substitute, simplify step by step to reach x² + y² + x + 2y = 0.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Let's break it down: solving fully: apply relevant formula, put numbers, compute. Result comes as R = (7, 7), (8, 8), (9, 9). Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Applying the basic concept, complete solution: write formula, plug data, do arithmetic. Final value matches Reflexive relation. Simple and accurate.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
The trick is using formula we get a * b = a + b. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get a * b = a + b.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
The trick is solving fully: apply relevant formula, put numbers, compute. Result comes as (2,3) ∈ R. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Simply put, after simplifying, sin-¹x is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
The trick is using formula we get Equivalence relation. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get Equivalence relation.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Understanding this is easy: we verify a * b = b * a by full calculation: use standard identity, substitute, simplify step by step to reach a * b = b * a.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Recall the rule complete solution: write formula, plug data, do arithmetic. Final value matches Surjective. Simple and accurate.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
Recall the rule after simplifying, -2 < k < 2 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
