If \(x = \{n^2+1:n\text{ is a positive integer and }1\leq n\leq 5\}\), \(y = \{5n:n\text{ is a positive integer and }1\leq n\leq 5\}\), find \(x\cap y\).
Question 1 Report
If \(x = \{n^2+1:n\text{ is a positive integer and }1\leq n\leq 5\}\), \(y = \{5n:n\text{ is a positive integer and }1\leq n\leq 5\}\), 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}.
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