Solveeit Logo
Login

Question

Question: Let \(A = \\{ x,y,z\\} \) and \(B = \\{ a,b,c,d\\} \). Which one of the following is not a relation ...

Let A=x,y,zA = \\{ x,y,z\\} and B=a,b,c,dB = \\{ a,b,c,d\\} . Which one of the following is not a relation from A to B.
1)(x,a),(x,c)1)\\{ (x,a),(x,c)\\}
2)(y,c),(y,d)2)\\{ (y,c),(y,d)\\}
3)(z,a),(z,d)3)\\{ (z,a),(z,d)\\}
4)(z,b),(y,b),(a,d)4)\\{ (z,b),(y,b),(a,d)\\}
5)(x,c)5)\\{ (x,c)\\}

Explanation

Solution

First, we will need to know about the concept of relation.
A relation MM is the subset of the cartesian product of M and N, where M and N are considered as two non-empty sets. It is concluded by stating their relationship between the first and second elements of the ordered pair.
Complete step-by-step solution:
Since from the given that we have two sets A=x,y,zA = \\{ x,y,z\\} and B=a,b,c,dB = \\{ a,b,c,d\\} we need to find their relation from A to B.
First staring with the option 1)(x,a),(x,c)1)\\{ (x,a),(x,c)\\} which is a relation from A to B because it consists of the elements in the A at the first and also the elements in the B at the second terms
Hence the option 1)(x,a),(x,c)1)\\{ (x,a),(x,c)\\} is incorrect because they are asking the not relation A to B.
Now we will go with the option 2)(y,c),(y,d)2)\\{ (y,c),(y,d)\\} which is a relation from A to B because it consists of the elements in the A at the first and also the elements in the B at the second terms
Hence the option 2)(y,c),(y,d)2)\\{ (y,c),(y,d)\\} is incorrect because they are asking the not relation A to B.
Now we will go with the option 3)(z,a),(z,d)3)\\{ (z,a),(z,d)\\} which is a relation from A to B because it consists of the elements in the A at the first and also the elements in the B at the second terms
Hence the option 3)(z,a),(z,d)3)\\{ (z,a),(z,d)\\} is incorrect because they are asking the not relation A to B.
Now we will go with the option 5)(x,c)5)\\{ (x,c)\\} which is a relation from A to B because it consists of the elements in the A at the first and also the elements in the B at the second terms
Hence the option 5)(x,c)5)\\{ (x,c)\\} is incorrect because they are asking the not relation A to B.
Finally take the option 4)(z,b),(y,b),(a,d)4)\\{ (z,b),(y,b),(a,d)\\} which is not the relation from A to B, because the set (a,d)(a,d) is only contained on the B. hence it is not the relation A to B as both the elements of the sets need to contain in the subset.
Therefore, the option 4)(z,b),(y,b),(a,d)4)\\{ (z,b),(y,b),(a,d)\\} is correct, because they are asking the not relation A to B subsets.

Note: Since a function is known as the relation only if each element of non-empty set M, has only one range to a non-empty set N.
Since if the question is about finding the relation function from A to B, then options like 1,2,3,51,2,3,5 are the correct options and thus the option 44 is incorrect. We need to be careful at the given question because correctly checking whether they are asking correct statements is incorrect as the requirements.