Consider numbers of the form a = a₁a2a3 . . . an, with n digits, each digit from the set {1, 2, 3, 4, 5, 6, 7, 8}. For example, if n = 4, the number a = a₁ª2a3a4 will have 4 digits from the set {1, 2, 3, 4, 5, 6, 7, 8}. Let n = 7. a. How many such numbers are there? b. How many such numbers are there for which the sum of the digits is even? c. How many such numbers contain more even digits than odd digits?

You have a set Y= { a, b, c, d, e}. How many ways can you arrange 2 elements of the set with repetition? List all of the outcomes. Enter your answer in the space provided below.

Consider the following set. {-5, -4, - . 0, 1, v2, 2, 2.5,4, 9} 0, 1, V2, 2, 2.5, 4, 9 Which numbers are even integers? (Select all that apply.) O -5 -4 1 1 V 2 2.5 4 9.

Given A={-4,0,11}, which elements of set are less than -1?

Let A = : {3, 4, 5, 6, 9}, Write down each of the following sets. (a) An B. (b) {b-2: be B and b+ 2 & A}. B = = {2, 3, 7, 8, 9, 10}. Now write down each of the following numbers. (c) The number of 3-element subsets of B. (d) The number of non-empty subsets of B. Describe all of the following sets by listing their elements. (e) The set of composite numbers less than 17. (f) (a ≤N Icm(a, 6) = 42}. (g) The set of complex numbers z such that z4 = 1. [No justification is required for any parts of this question.]

Express the set in roster form. B= {x | xEN and x26} ..... Choose the correct answer below. O A. B= (7, 8, 9, 10, .} O B. B= {6, 7, 8, 9, ., 100} OC. B= {6, 7, 8, 9, ..} O D. B= {6} O E. B= {6, 7, 8, 9} OF. B= (7, 8, 9, 10} O G. B=Ø

Is {2,2}={2, {2} }? How many elements are in the set {a,a,a,a,a}? {x€N|xis greater than 10 and x is divisible by 3} {x€Z|x is prime and x is divisible by 2} {X c is eqaul to z| x squared = 4}

Let 1 = (1, 2, 3, 4, 5, 6, 7, 8, 9}. If five integers are chosen from T, must there be two integers whose sum is 10? If the answer is yes, enter YES in the blank. If the answer is no, use set- roster notation to fill in the blank with a set of five numbers from T, no two of which have a sum of 10.

Consider the following set. {-5, -2, -4/3, 0, 1, V3, 2, 2.25, 3, 8} Which numbers are rational numbers? (Select all that apply.) -5 -2 -4/3 1 O V3 2.25 3 8

List all the ways to select two members from S with repetition. The order in which the members are selected is not important. For example, DD is allowed and BA is the same selection as AB. S= {H, J, K, L, M} ....D Identify the list of all the ways to select two members from S, allowing for repetition. Choose the correct answer below. O A. HH, HJ, HK, HL, HM, JJ, JK, JL, JM, KK, KL, KM, LL, LM, MM O B. HH, HJ, HK, HL, HM, JK, JL, JM, KL, KM, LM OC. HH, HJ, HK, HL, HM, JH, JJ, JK, JL, JM, KH, KJ, KK, KL, KM, LH, LJ, LK, LL, LM O D. HK, HL, HM, JK, JL, JM, KL, KM