#discrete math

Sets, Relations and Functions

Which of the following relations is reflexive but not transitive for the set T = 7, 8, 9?

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

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Sets, Relations and Functions

(a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?

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

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Sets, Relations and Functions

Let ‘*’ be defined on the set N. Which of the following are both commutative and associative?

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

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Sets, Relations and Functions

Let R be a relation in the set N given by R=(a,b): a+b=5, b>1. Which of the following will satisfy the given relation?

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

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Matrices and Determinants 3

Which of the following relations is symmetric but neither reflexive nor transitive for a set A = 1, 2, 3.

Think of it like this: using formula we get R = (1, 2), (2, 1). Calculation gives this directly, check steps: apply rule, substitute values, simplify to get R = (1, 2), (2, 1).

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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