Question

Describe the sets given below using the Roster Method (list all elements of a set in curved brackets). (i) The set of all even perfect squares less than 100 . (ii) The set of all natural numbers x such that x<100 and both x+1 and x−1 are prime. (iii) {x∣x2+x=42}. (iv) The set of all numbers that are neither positive nor negative.

Answer 1

The set of even perfect squares less than 100 is {4, 16, 36, 64}. The set of natural numbers x such that x<100 and both x+1 and x−1 are prime is {2, 11, 29, 41, 59, 71, 89}. The set {x∣x^2+x=42} is {-7, 6}. The set of numbers that are neither positive nor negative is {0}.

Step-by-step explanation:

(i) The set of all even perfect squares less than 100 can be represented as {4, 16, 36, 64}. Since we want even perfect squares, we only consider numbers that are the square of an even number. For example, 2 squared is 4, 4 squared is 16, and so on.

(ii) The set of all natural numbers x such that x<100 and both x+1 and x−1 are prime can be represented as {2, 11, 29, 41, 59, 71, 89}. We check each number less than 100 and find the ones that satisfy the condition.

(iii) The set {x∣x^2+x=42} can be represented as {-7, 6}. We solve the equation x^2 + x = 42 to find the values of x that satisfy the condition.

(iv) The set of all numbers that are neither positive nor negative can be represented as {0} since 0 is neither positive nor negative.