Home
Class 12
MATHS
Let S be a set of all distinct numbers o...

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

Text Solution

Verified by Experts

As `1/2,2/4, 3/6 ` are same and `1/1,2/2,3/3,...` are same.
We will find only co-prime numbers.
So, when `p = 1,q = {1,2,3,4,5,6}`
So, total elements in `S` in this case ` = 6`
When `p = 2, q = {1,3,5}`
So, total elements in `S` in this case `= 3`
When `p = 3, q = {1,2,4,5}`
So, total elements in `S` in this case `= 4`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If A={1, 3, 5, 7}, then what is the cardinality of the power set P(A)?

If A = (1, 3, 5, 7), then what is the cardinality of the power set P(A)?

The number of rational numbers (p)/(q), where p,q in[1,2,3,4,5,6} is

Find the number of distinct rational numbers x such that o

Find the number of distinct rational numbers x such that o

Find the number of distinct rational numbers x such that oltxlt1 and x=p//q , where p ,q in {1,2,3,4,5,6} .

Find the number of distinct rational numbers x such that oltxlt1 and x=p//q , where p ,q in {1,2,3,4,5,6} .

Find the number of distinct rational numbers x such that o < x < 1a n dx=p//q , where p ,q in {1,2,3,4,5,6} .

Let a,b,c,d are distinct numbers to be chosen from the set {1,2,3,4,5}. If the least possible positive solution for x to the system of equations ax+by=1cx+dy=2} can be expressed in the form (p)/(q) where p and q are relatively prime,then find the value of (p+q).

Find the number of distinct rational numbers x such that 0 lt x lt1 and x=p//q , where p ,q in {1,2,3,4,5,6} .