Case Study Challenge
Debate Competition: Mapping Speakers & Judges
A school is organizing a debate competition with participants as speakers
S = {S₁, S₂, S₃, S₄} and these are judged by judges
J = {J₁, J₂, J₃}.
Each speaker can be assigned one judge. Let R be a relation from set S to J defined as
R = {(x, y) : speaker x is judged by judge y, x ∈ S, y ∈ J}.
Answer the following based on the above:
| (i) | How many relations can be there from S to J? | [1 Mark] |
| (ii) | A student identifies a function from S to J as f = {(S₁, J₁), (S₂, J₂), (S₃, J₂), (S₄, J₃)}. Check if it is bijective. | [1 Mark] |
| (iii) | (a) How many one-one functions can be there from set S to set J?
— OR —
(b) Another student considers a relation R₁ = {(S₁, S₂), (S₂, S₄)} in set S. Write minimum ordered pairs to be included in R₁ so that R₁ is reflexive but not symmetric. |
[2 Marks] |