If x = {n2+1:n is a positive integer and 1 ≤ ≤ n ≤ ≤ 5}, y = {5n:n is a positive integer and 1 ≤ ≤ n ≤ ≤ 5}, find x ∩ ∩ y.

If x = {n2+1:n is a positive integer and 1 $\le$ n $\le$ 5}, y = {5n:n is a positive integer and 1 $\le$ n $\le$ 5}, find x $\cap$ y.

Answer Details

To find the intersection of two sets, we need to find the elements that are common to both sets. First, let's find the elements of set x: x = {n² + 1 : 1 ≤ n ≤ 5} If we substitute each value of n from 1 to 5 into the formula n² + 1, we get the following values for set x: x = {2, 5, 10, 17, 26} Now, let's find the elements of set y: y = {5n : 1 ≤ n ≤ 5} If we multiply each value of n from 1 to 5 by 5, we get the following values for set y: y = {5, 10, 15, 20, 25} To find the intersection of sets x and y, we need to find the elements that are common to both sets. From the values listed above, we can see that the elements 5 and 10 are in both sets x and y. Therefore, the intersection of x and y is: x ∩ y = {5, 10} Therefore, the correct option is {5, 10}.