Question

(a) If \( A = \{1, 2, 3\} \), \( B = \{4, 5\} \), then find the number of relations from \( A \) to \( B \):

Hint:

The total number of relations is \( 2^{m \cdot n} \), where \( m \) and \( n \) are the sizes of the sets \( A \) and \( B \), respectively.

Answer 1

The number of elements in \( A \) is \( |A| = 3 \) and in \( B \) is \( |B| = 2 \).
The total number of relations from \( A \) to \( B \) is given by: \[ 2^{|A| \cdot |B|} = 2^{3 \cdot 2} = 2^6 = 64. \]