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Question
Read the following passage:
|
An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. |
Based on the above information, answer the following questions:
- How many relations are possible from B to G? (1)
- Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
- Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
OR
A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)
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Solution
- Number of possible relations from B `rightarrow` G
= `2^(n(B) xx n(G))`
= 23 × 2
= 26
= 64. 
Every element of set B has two options to map in set G i.e., B1 can go to G1 and G2.
So, 2 ways (i.e., two functions).
∴ Total function = 2 × 2 × 2 = 8- R : B `rightarrow` B
R = {(x, y) : x and y are students of the same sex}
(b1, b1) ∈ R ...(Reflexive)
(b1, b2) ∈ R `\implies` (b2, b1) ∈ R ...(Symmetric)
If (b1, b2) ∈ R ∧ (b2, b3) ∈ R
`\implies` (b1, b3) ∈ R ...(Transitive)
`\implies` It is an equivalence relation.
OR
Given, B = {b1, b2, b3} and G = {g1, g2}
f = {(b1, g1), (b2, g2), (b3, g1)}
Since b1 and b3 both are related to same element g1.
So f is not bijective (one-one).
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