Let and let be the set of prime numbers less than

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

A = \{1, 2, 3, 4\}

and let

B

be the set of prime numbers less than

15

. A relation

T \subseteq A \times B

is defined as follows: For every

a \in A

(a, b) \in T

where

b

is the smallest prime number strictly greater than

2a

. Answer the following: (i) Construct the set

T

by listing all its ordered pairs. (ii) Prove that

T

is a function from

A

B

. (iii) Determine whether this function is one-one, onto, both or neither. Give reasons for each conclusion.