Discrete Mathematics Answers

Find the Transitive closure by using Warshall’s Algorithm where A= {1, 2, 3,
4, 5, 6} and R= {(x,y)| (x-y)=2}

There are two webcams, X and Y that can automatically switch On or Off at any given time to record
a live video streaming session. To ensure the smooth recording session, the live feed input system
is programmed with certain criteria. The conditions set are; if webcam X and webcam Y are switch
on, the input system can enable the recording input and the live session will start. If either webcam
X or webcam Y is switched on, the input system cannot enable the recording and the live session
will stop. In all other conditions, the input system will enable the recording and the live session
streaming will commence.
a. Based on the scenario above, generate a simple pseudocode with a function that has x and
y as inputs and livestream and nolivestream as outputs.

How many 4-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5 if the first digit must not be 0 and repetition of digits is not allowed?
a.300
b.320
c.360
d.280

How many distinct permutations are there of the letters of the word "MARRIAGE"?
a.30240
b.40320
c.20160
d.10080

Suppose S is a set containing 5 elements, and that ⪯ is a total ordering of S. Draw the Hasse diagram for ⪯ (no need to label the vertices in your diagram).

Let S={1,2,3,4}, and define a partial ordering of P(S) (the power set of S), by: A⪯B if and only if A⊆B. Is this partial ordering in fact a total ordering (chain)? Why or why not?

Let p and q be distinct positive primes. Define the partial ordering ⪯ of S={1, p, p^2, p^3, p^4, q, q^2, q^3, q^4} as follows: a⪯b if and only if a|b. Draw the Hasse diagram for this partial ordering of S.

Suppose S is a set, and P={S} is a partition of S. Find the equivalence relation R corresponding to P.

Let S ={a, b, c, d, e}, and P={{a, b},{c, d},{e}}.
(a) Verify that P really is a partiton of S.
(b) Find the equivalence relation R on S induced by P.

Let S be the set of bit strings of length no larger than 6, and define an equivalence relation R on S as follows: (x, y) ϵ R if and only if x and y are of the same length. Specify the partition P of S that arises from R.