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Consider the following relations from A to B where A = {u, v, w, x, y, z} and B = {p, q, r, s}. 1. {(u, p}, (v, p), (w, p), (x, q), (y, q), (z, q)} 2. {(u, p), (v, q), (w, r), (z, s)} 3. {(u, s), (v, r), (w, q), (u, p), (v, q), (z, q)} 4. {(u, q), (v, p), (w, s), (x, r), (y, q), (z, s)} Which of the above relations are not functions?

Consider the following relations from A to B where A = {u, v, w, x, y, z} and B = {p, q, r, s}. 1. {(u, p}, (v, p), (w, p), (x, q), (y, q), (z, q)} 2. {(u, p), (v, q), (w, r), (z, s)} 3. {(u, s), (v, r), (w, q), (u, p), (v, q), (z, q)} 4. {(u, q), (v, p), (w, s), (x, r), (y, q), (z, s)} Which of the above relations are not functions? Correct Answer 2 and 3

Concept:

A relation from a set X to a set Y is called a function if

  • Each element in the set X has its image in set Y. 
  • It is also possible that these are few elements in set y which are not the image of any element in set X. 
  • Every element in set X should have one and only one image.

 

Calculation:

Given that, A = {u, v, x, y, z); B = {p, q, r, s}

As we know, a mapping f: x + y is said to be a function,

1. [ alt="F1 Aman.k 26-08-2020 Savita D5" src="//storage.googleapis.com/tb-img/production/20/08/F1_Aman.k_26-08-2020_Savita_D5.png" style="width: 182px; height: 173px;">

Its a function

2. [ alt="F1 Aman.k 26-08-2020 Savita D6" src="//storage.googleapis.com/tb-img/production/20/08/F1_Aman.k_26-08-2020_Savita_D6.png" style="width: 182px; height: 173px;">

Here, each elements in A has not its image in B, so its not a function

3. [ alt="F1 Aman.k 26-08-2020 Savita D7" src="//storage.googleapis.com/tb-img/production/20/08/F1_Aman.k_26-08-2020_Savita_D7.png" style="width: 182px; height: 173px;">

Here, each elements in A has not its image in B, so its also not a function

4. [ alt="F1 Aman.k 26-08-2020 Savita D8" src="//storage.googleapis.com/tb-img/production/20/08/F1_Aman.k_26-08-2020_Savita_D8.png" style="width: 182px; height: 173px;">

Its a function

 

Hence, option (3) is correct.

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