1. (a ) (5 points) Use the Binomial Theorem to write the coefficient of the term

Question

1. (a ) (5 points) Use the Binomial Theorem to write the coefficient of the term x4 y5 in the   expansion of (x + y) 9?

         (b) (5points) Write the coefficient of the term x2y4z5 expansion of (x + y + z) 11. See example 12 in your notes of SU week7 (week 10)

2. (i) (5 points)

Let a stand for the airport in the city of Manchester, let b stand for the airport in Boston, c stand for the Chicago airport, d for the airport in the city of Denver. Is their a flight from Manchester to Chicago?

3. (ii) (10 points)

Compute and interpret the Boolean products: MR 2, and MR 3. (Remember to use Boolean arithmetic)

4. (iii) (10 points)

Now call the given matrix A and compute A2 and A3 using regular, not Boolean arithmetic. What do these products give you?

5. (iv) (5 points)

Note on page 602, Theorem 2 gives the transitive closure of a relation. Since MR is a

4 x 4 matrix for this problem we have

MR* = MR MR 2 MR 3 MR 4    which is also frequently written as

MR* = MR + MR 2 + MR 3 + MR 4   (where the + is Boolean addition)

In a sentence or two briefly explain what MR* = MR + MR 2 + MR 3 + MR 4    means for this problem.

Explanation / Answer

1)a)9c4= 9*8*7*6/4*3*2*1=126

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