3. For each of the following entities, say whether it is a member of P(N), and explain why or why not. (a) 5 (b) {5} (c) {3, 100, 365} (d) {{3}, {100, 365}, {1000, 2000, 2001}} f the following two tynes:

Problem 16. Construct a matrix with the required property or say why that it is impossible. 1 2 (a) Column space contains 2 and-3, and nullspace contains 1 -3 5 22 1 2 (b) Row space contains 2 and -3, and nullspace contains 5 1 (c) Ax = 1 has a solution and AT 0 H 0 = [B] 0 0

it's saying this is an invaild notation. for both.

. Let a = 1 2 3 4 5 6 2 1 4 5 6 3 and B = 1 2 3 4 5 6 1 3 2 65 4 :) (a) Find a B(2). Find 6-¹(2). (b) Find a B. State the answer in the array notation. (c) Find 6-¹. State the answer in the array notation. (d) Find a³. State the answer in the array notation. (e) Find 3-2. State the answer in the array notation. be permutations.

Evaluate Select one: O a. O b. Od. x+3 x²+x-2 2x+5 X x²+4x+4 (2x+5)(x-1)(x+2) x²+4x+4 2x²+11x+15 x+2 (2x+5)(x-1) rả 5x17 (2x+5)(x-1)(x+3) What are the non-permissible values for 1+1

15. Which of the following division statements are equivalent to (6) 3 = -18? (i) 18 + 3 = 6 (ii) 18 3 = 6 (iii) 18 + 6 = -3 (iv) 18 +6 = 3 A) None B) (ii) and (iii) C) (i) and (iv) D) (ii) and (iv)

If n(A) = 101, n(A ∪ B) = 144, and n(A ∩ B) = 49, find n(B).

28. In Example 9.7.5 it was shown that (a + b) = a* + 5a*b + 10a b² + 10a²b³ + 5ab* + b35. %3D Evaluate (a + b) by substituting the expression above into the equation (a + b) = (a + b)(a + b)³ and then multiplying out and combining like terms.

Note: The notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 1.) Evaluate without a calculator, and show your work: (a) C(12, 5) (b) C(9,6)

If  n(A) = 108, n(A ∪ B) = 160, and n(A ∩ B) = 47, find n(B)