Relations and Functions — Important Questions
ICSE · Class 12 · Mathematics
104 important questions from Relations and Functions for ICSE Class 12 Mathematics, with answers. Includes multiple choice and true false questions.
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Important Questions from Relations and Functions
A relation R on a set A is transitive if:
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(a,b),(b,c) ∈ R ⟹ (a,c) ∈ R
Transitivity: if a relates to b and b relates to c, then a must relate to c.
The identity relation on any set A is always reflexive.
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True
The identity relation I_A = {(a,a): a ∈ A} contains all diagonal pairs, so it is reflexive by definition.
The empty relation on any non-empty set A is symmetric.
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True
Since the empty relation has no pairs at all, the symmetric condition (a,b)∈R ⟹ (b,a)∈R is vacuously true.
The universal relation on a set A means:
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R = A × A
The universal relation contains every possible ordered pair from A × A, so R = A × A.
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