Question

Let S be a set of all distinct numbers of the form `p/q`, where p, `q in{1, 2, 3, 4, 5, 6}`. What is the cardinality of the set S
A. 21
B. 23
C. 32
D. 36

Answer 1

Correct Answer - B
Given that p, q: (1, 2, 3, 4, 5, 6,)
For `(p)/(q)` form, when p=1, q=1, 2, 3, 4, 5, 6
thus, `(p)/(q)=1, (1)/(2),(1)/(3),(1)/(4),(1)/(5) and (1)/(6)`
`n=((p)/(q))=6`
When p=2, q=1, 3,5
thus `(p)/(q)=2, (2)/(3), (2)/(5) and n((p)/(q))=3`
When p=3, q=1, 2, 4, 5
thus `(p)/(q)=3, (3)/(2),(3)/(4),(3)/(5) and n((p)/(q))=4`
When p=4, q=1,3,5
thus `(p)/(q)=4, (4)/(3), (4)/(5) and n((p)/(q))=3`
When p=5, q=1,2,3,4,6
thus `((p)/(q))=5, (5)/(2), (5)/(3), (5)/(4) and (5)/(6) and n((p)/(q))=5`
When P=6, q=1, 5
thus `((p)/(q))=6, (6)/(5) and n((p)/(q))=2`
Hence, cardinality of the set (s)
=6+3+4+3+5+2=23.