Question

1. Use the roster method to describe the elements of the following set.

x∈ℤ||x−3|<12 and x is a multiple of 3

2. Use the roster method to describe the elements of the following set.

{n∈ℕ∣∣∣1n+6⩾6272 and n is a multiple of 5}

3. Determine the cardinality of the following sets.

{x∈ℤ|−4⩽x⩽3}:

{x∈ℕ|−4⩽x⩽3}:

4. Evaluate the following expressions. [Hint: start by factoring the polynomial.]

∣∣{x∈ℚ∣∣18x3+69x2+56x=0}∣∣=

∣∣{x∈(0,∞)∣∣18x3+69x2+56x=0}∣∣=

∣∣{x∈ℤ∣∣18x3+69x2+56x=0}∣∣=

5.  Evaluate the following expressions. [Hint: start by factoring the polynomial.]

∣∣{x∈ℝ∣∣x4+11x2+28=0}∣∣=

∣∣{x∈ℚ∣∣x4+11x2+28=0}∣∣=

∣∣{x∈ℕ∣∣x4+11x2+28=0}∣∣=

6.

Let A={1,2,3,4,5,6,7} and B={1,3,4,6}. List all sets C such that C⊆A and B⊆C.

Enter your answer as a list of sets separated by commas, e.g.: {a},{a,b}.

7.

Let A={0,{∅}}. Determine whether the statements below are true or false.

Enter T for true and F for false.

  1. ∅∈A
  2. ∅∈℘(A)
  3. {0,∅}⊆A
  4. ∅⊆A

Answer 1