Discrete Mathematics Answers

Simplify ((A U B') n C) U(A'n B)' and write the dual of the result.

Suppose that 40 Malaysian Chinese are surveyed and they speak at least one of the

three dialects, Cantonese, Hokkien or Hakka. It is found that 30 of them speak

Cantonese, 20 speak Hokkien and 15 speak Hakka. It is also found that 3 of them speak

all three dialects. How many of the surveyed Malaysian Chinese speak exactly two

languages?

Let A, B and C are sets. Prove that ≤ is transitive.                                                       (5 marks)

Let P(x), Q(x) and R(x) are propositions and the universe of discourse; all students; P(x) = x is intelligent Q(x) = x has solved the problem R(x) = x has clearly understood the clues

In any case, if you somehow could not attend the Discrete Mathematics final exam then you will not be able to pass out the course and if you have the fever then you will not be able to pass out the course Construct the proposition by your own. Determine whether the preposition is tautology, contradiction or contingency and explain the answer by your own words. Make sure that you’re not copy from others. 

1. Given the following:

• g: "You can graduate.

• m: 'You owe money to the college."

. r: "You have completed the requirements of your major."

• b: "You have an overdue book."

Translate "You can graduate only if you have completed the requirements of your major, you do not owe money to the college, and you do not have an overdue book" into a propositional logic.

2. Show that -p → (q + r) and q→ (p V r) are logically equivalent.

3. Show, by the use of the truth table (truth matrix), that the (pvq)v [(-p)^(q)] is a contradiction.

Using quine mccluskey to simplify the sum of product expansion wxyz'+wx'yz+wx'yz'+w'xyz+w'xy'z + w'x'yz + w'x'y'z

define the relation on A={1,2,3} such that aRea of a=b+1 and find it's domain and range

define the relation on A={1,2,3} such that aRea of a=b+1

a.      Let A and B and C be sets, prove that A∩(BUC) = (A∩B)U( A∩C).