concepts of sets

Its easier to list elements of S first

S contains squares of all odd numbers

S - {1,9,25,49,-------} - Squares of 1,3,5 and 7 respectively.

R contains odd numbers < 50 : R - {1,3,5,7,9..,25,... , 49}

Clearly 4 elements intersect. C IMO

R would contain : (1,3,5,7,9,11,...............49)
S would contain : (1,9,25,49, 81.............................2401)

Intersecting Set : (1,9,25,49)

The answer is 4...

The question is really asking how many odd numbers between 1 and 50 are perfect squares. We know that the numbers in set S will go significantly higher than 50 but set R is constrained by having a max of 50 thus we only have to look at those.

List the squares to 50 (will only be the squares of integers up to 7)
1, 4, 9, 16, 25, 36, 49

Which of these are odd - 1, 9, 25 & 49 thus there are 4 intersections.

Best of Luck

romitvsingh wrote:R is the set of positive odd integers less than 50, and S is the set of the squares of the integer in R, How many element does the intersection R & S contain?

a) none
b) two
c) four
d) five
e) seven

pls explain in detail

R is the set of positive odd integers less than 50 & S is the set of the squares of the integer in R

So we need to simply find out the odd positive squares upto 50 , which are as follows...

1 , 9 , 25 ,49