Discrete Mathematics Answers

2. Conditional equivalence. Which of the following implications are true?
a) If 2 + 2 = 5 then 2 + 2 = 6.
b) If 2 + 2 = 4 then the world is flat.
c) If both of the previous statements are true then 2 + 2 = 7.

Q1. Propositions. Which of the following sentences are propositions?
a) It rained yesterday.
b) The last digit of the smallest prime number larger than 100100 is 1.
c) This sentence is false.
d) 6 + 5 = 10.

Show that 1+(1/√2)+...+(1/√n)>= √2 √(n-1) , for n belongs to N , n>1.

Which of the following statement are True?1.(A/B) union C = A / (B intersection C) for any three sets A , B and C .?

An integer solution to the equation 3x+4=7y is an ordered pair of integers (x, y) that satisfies the equation. For example, (1,1) is one such solution. Write the set of all integer solutions to the equation 3x + 4 = 7y in set builder notation.

Prove that if n or m is an odd integer, then n*m is an even integer.

Proposed proof: Suppose that n or m are even. Then n = 2k and m = 2j for some integers k and j. This shows that n*m = (2k)*(2j) = 4k*j. Therefore, n*m is even.

Proposed proof: Suppose that n or m are even. Then n = 2k and m = 2j for some integers k and j. This shows that n*m = (2k)*(2j) = 4k*j. Therefore, n*m is even

1. In how many ways can 30 identical balls be distributed into 7 distinct boxes (numbered box 1, ... , box 7) subject to the following conditions.
(a) With no constraints.

Solve this degeneracy problem
11 〖2 〗^8 8 〖6 〗^6 〖2 〗^4 Supply
〖9 〗^10 9 12 9 6 18
7 6 〖3 〗^8 7 7 10
〖9 〗^2 3 5 〖6 〗^2 11 8
Demand 12 8 8 8 4 4

Solve by NWCM (north-west corner method) and find optimal solution by UV method
3 1 7 4 Supply
2 6 5 9 250
8 3 3 2 350
Demand 200 300 350 400