Discrete Mathematics Answers

For the language L = {acnb | n > 0 }, which one of the following strings is not a part of the language ?

Use the symbols ~, ^ and v, and write the following statements.

both p or q and r

2. Produce truth tables for given Boolean expressions.


i. A̅ B̅ C+A B̅ C̅ + ABC +A̅ B C̅

ii. (A+B̅+C)(A+B+C)(A̅+B+C̅)

List all elements of the following sets as a set. All answers must be exact and not rounded

1.{q is an integer | q is a factor of 231}


Describe the following sets using proper set-builder notation as explained in your book. You may not simply list the numbers

1. {1, 9, 27, 81, 243, 729}

2. The rational numbers that are strictly between -4.1 and 3.2

3. The negative even integers that are multiples of 7


Let A = {a, b, c, 1, 2, 3, q, r, s}, B = {a, 1, r}, and C = {a, 3, q, x, y, z}. Which of the following statements are true? Which are false? Explain your answers.

1. 3 ∈A

2. z ∈A

3. B ⊂A

4. {1,3}∈A

5. {1,3}⊂A

6. A ⊂A

7. B ⊆B

8. ∅ ⊆C


Let A, B, and C be as in #4 and let U = {1, 2, 3, 5, 7, 8, 9, a, b, c, d, e, f, g, x, y, z}. Determine:

1. A ∩B

2. A ∩C

3. A ∪B

4. A ∪C

5. A-B

6. A -C

7. B-A

8. C-A

9. A^C

10 .A⨁C

Give partimos of R having (a) one block, (b) two blocks, (c) three blocks, (d) infinity many blocks

1. Develop truth tables and its corresponding Boolean equation for the following scenarios. i. ''If the driver is present AND the driver has NOT buckled up AND the ignition switch is on, then the warning light should turn ON.'' ii. If it rains and you don't open your umbrella then you will get wet.

1. Develop truth tables and its corresponding Boolean equation for the following scenarios.

i. ''If the driver is present AND the driver has NOT buckled up AND the ignition switch is on, then the warning light should turn ON.''

ii. If it rains and you don't open your umbrella then you will get wet.

given 2 sets A and B, use membership table to show that (A-B)∪(B-A)=(A∪B) -(A∩B)

Use mathematical induction to prove that ∀n∈N


P(n):1·2·3+2·3·4+···+n(n+1)(n+2)=n(n+1)(n+2)(n+3)/4

how many choice function we could we define on the set X

X= {{0,1},{2,3},{4,5}}