Question

List the elements of each of the following sets by using the roster method. (a) The set of all days in a week that begin with the letter T. (b) The set of all positive integers less than 12 and greater than or equal to 6 . (c) The set of all positive integers greater than 12 or less than or equal to 6 . (d) The set of all positive integers greater than 12 and less than or equal to 6. (e) {x∣x∈N,x is odd, and x<15} (f) {x∣x∈Z and 2x²+5x−3=0} (g) {x∣x∈Q and 2x²+5x−3=0} (h) {z∣z∈C and z⁴=1} (i) {(x,y)∣x∈Z,y∈Z, and 0

Answer 1

The set of all positive integers greater than 12 and less than or equal to 6 is an empty set.

Step-by-step explanation:

(d) The set of all positive integers greater than 12 and less than or equal to 6 is an empty set. This is because there are no positive integers that are simultaneously greater than 12 and less than or equal to 6.

Therefore, the roster method for this set is {}.