Which of the following models are counter-models that shows that is not a logical consequence? Select one or more: □ D = {a,b}, P¹ = {(a,b), (b, b)}, Q¹ = {b}. OD=N₁ P¹ = {(n,n+ 1) : n € N}, Q¹ = {n € N:n is even}, where N = {0, 1, 2,...} denotes the natural numbers. □ D = {a,b}, P¹ = {(a, a), (b,b)}, Q¹ = {a}. □ D = {a,b,c}, PI = {(a,b), (b, c), (c, a)}, Q¹ = {a,b,c}. ○ D = N₁ P¹ = {(n, 2n) : n ≤ N}, Q¹ = {n € N:n is even}, where N = {0, 1, 2,...} denotes the natural numbers. VryP(x, y), Vr(yP(x,y) → Q(x)) ¥ VIQ (1)

2. Find |A-'A"BA¬| where -2 1 4 -1 -4 -1 1 3 1 3 5 A = 5 В -1 2 1 -1 2 -1 -7 1 4 2 -3 7

9

2 11 5,D = -1 -2) 3 3 1] 4. 5] 6. Let, A =| 3 -4 1 -1 Now if AD=B, Then b32 =?

Let Aį = [i, i + 1], i = 1, 2, 3, .…... Then A₁ A₂ A3 A4 is. a. {1,2,3,4,5} b. (1,5) C. {} d. [1,5]

compute (BA)T

What is the end behavior of each of the following 1. y = -4x3 + 2x? + 7 2. y = 2x3 - 3x6 + 4 3. y = -x³ + 2x5 – 1 4. y =Ox (x - 7)(x + 5)* 5. y = x(x + 1)(x - 8)

5. Use a table to express the values of each of these Boolean functions. а) F(x, у, 2) %3DХу b) F(x, y, 2) —х + уz с) F(x, у, 2) —ху+ (хуг) d) F(x, y, 2) — x(уz + у2)