Choose the correct solution in roster form.S is the set of prime numbers that are less than 15.

A- { 2, 3, 5, 7, 11, 13 }
B- { 2, 3, 5, 7, 9, 11, 13 }
C- { 1, 3, 5, 7, 9, 11, 13 }
D- { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }

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Write the solution to the inquality in set-builder notation.

9t - 4 >32

A- { t | t > 4 }
B- { t | t > 6 }
C- { t | t > 28 }
D- { t | t > 36 }

Mathematically speaking, roster form of a set is a list of elements that are in the set.

Basically, to represent a set in roster form, we simply list the elements of the set, separated by commas, within braces.

as per the question, consider the set, S, described verbally:

   S = {all prime numbers less than 15}

To write this in roster form, we would first identify all the elements in the set. Let's see. . . the integers that are strictly greater than 0 and less than or equal to 4 would be the integers that are between 0 and 4, not including 0, but including 4, so 1, 2, 3, and 4.

Now we just write these integers, separated by commas, within braces.

S = {2, 3, 5, 7, 11, 13}. So answer is option A

Set notation is a representation of a set of the form {element | properties of that element}.

To represent the inequality in set builder notation, we will first have to solve for the inequality as follows:

9t - 4 >32

Step 1: Add 4 on LHS(Left hand side) and RHS(right hand side) of the inequality.

9t > 36

Step 2: Divide LHS and RHS by 9

t > 4

This means that the inequality holds for all values of t greater than 4 i.e.

{ t | t > 4 }. so answer is option A