4. Six women and eight men are on the faculty in the mathematics department at a...

   

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4. Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the 1. Solve the congruence: 2x = 5(mod 11) а. 5 b. 6 с. 7 d. 8 department if at least one woman must be on the committee? a. 4242 b. 126 2. Find f(4) if f is defined recursively by: f(0) = f(1) = 1 and f(n) = f(n-1) + f(n-2) for n > 1. с. 931 d. 1131 а. 5 b. 25 5. True of False? a, = 2 a solution to the recurrence с. 33 d. 1214 relationa, = 2a, -a,, with initial conditions a, = 2 and . az = 2 a. True b. False 3. Find the sequence for the recursive formula: s, =-+9, So =-3 а. 14, -4, 14, -4 b. 6, 14, 86, 734 с. -3, 12, -3, 12 d. -3, 9, -3, 9 6. Find a solution to the recurrence relation: a, = 3na1»a, = 2 a. a, = 3" - n! b. a, = 2.3" - n! C. a, = 2.3" -n d. a, =2-3" 7. A connected planar graph has 28 edges. If a planar representation of this graph divides the plane into 16 regions, how many vertices does the graph have? а. 14 b. 12 с. 10 d. None of the above 8. True or False? The following relation is an equivalence relation: {(0,1),(1,1),(2,1),(3,3)}. a. True b. False 4. Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the 1. Solve the congruence: 2x = 5(mod 11) а. 5 b. 6 с. 7 d. 8 department if at least one woman must be on the committee? a. 4242 b. 126 2. Find f(4) if f is defined recursively by: f(0) = f(1) = 1 and f(n) = f(n-1) + f(n-2) for n > 1. с. 931 d. 1131 а. 5 b. 25 5. True of False? a, = 2 a solution to the recurrence с. 33 d. 1214 relationa, = 2a, -a,, with initial conditions a, = 2 and . az = 2 a. True b. False 3. Find the sequence for the recursive formula: s, =-+9, So =-3 а. 14, -4, 14, -4 b. 6, 14, 86, 734 с. -3, 12, -3, 12 d. -3, 9, -3, 9 6. Find a solution to the recurrence relation: a, = 3na1»a, = 2 a. a, = 3" - n! b. a, = 2.3" - n! C. a, = 2.3" -n d. a, =2-3" 7. A connected planar graph has 28 edges. If a planar representation of this graph divides the plane into 16 regions, how many vertices does the graph have? а. 14 b. 12 с. 10 d. None of the above 8. True or False? The following relation is an equivalence relation: {(0,1),(1,1),(2,1),(3,3)}. a. True b. False

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1 The equation 2x5mod 11 means 2x511n for some integer n Here x too is an integer By taking n0 we get 2x5 but no integer x satisfies this equation Tak... View the full answer