Question

Consider the following relations from A to B where A = {u, v, w, 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 ?

• A. 1 and 2
• B. 1 and 4
• C. 2 and 3
• D. 3 and 4

Answer 1

The correct option is D 3 and 4

For a relation to be a function, every element in set $A$ should have a image in set $B$,

But no element of set $A$ can have more than one image.

In 1 and 2, all elements of $A$ has only one image in $B$.

In 3,

The element $u$ has two images $p$ and $s$, which violates the condition of functions.

In 4,

Elements $x$ and $y$ are not the part of set $A$, hence it is not a function.

Hence, D is correct.