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In a school 100 students have access to three software packages A, B, C.
Where 28 didn’t use any software, 8 used only package C, 26 used only package
A,7 used package B, 10 used all three packages, 13 used both A and C
a) Draw a Venn diagram with all sets enumerated as for as possible.
b) If twice as many students used package A as Package C, write down a pair
of simultaneous equations in x and y.
c) Solve these equation to find x and y.
d) How many students used package B.
Simplify the Boolean Function using K Map (5 pts each) and draw the logic diagram (5 pts each)
a. F(a, b, c) = ∑ (0, 1, 2, 4, 5, 7)
b. F(a, b, c, d) = ∑ (0, 1, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14)
c. F (w, x, y, z) = ∏ (1, 2, 7, 11, 13, 15)
Simplify the Boolean Function using K Map (5 pts each) and draw the logic diagram (5 pts each)
a. F(a, b, c) = ∑ (0, 1, 2, 4, 5, 7)
b. F(a, b, c, d) = ∑ (0, 1, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14)
c. F (w, x, y, z) = ∏ (1, 2, 7, 11, 13, 15)
Calculate the number of vertices in a full 5-ary tree with 45 internal vertices.Also find out the number of leaves.
Exhibit a cycle of length 9 in this graph
1.Find a possible statistical problem inside your home relating to a discrete random variable lesson, explain in a paragraph form…..(2-3 sentence will do)
2.Find the possible random variable
3.Create a probability distribution
4.Compute for the mean variance and standard deviation
5.Interpret result
6.Conclusion
Let A be a set and B be some fixed subset of A. Define a relation R on P(A) as follows:
X1RX2 iff X1 U B = X2 U B
for all X1, X2 in P(A). It is known that R is an equivalence relation on P(A).
For A = N and B = {1, 2}, enumerate the elements of [{2, 3}]R.
- Prove that 7n−17n−1 is a multiple of 6 for all n∈N.
- Use induction to prove for all n∈Nn∈N that n∑k=02k=2n+1−1.
- Prove that (ab)n=anbn(ab)n=anbn is true for every natural number n
#331389 on Nov 2022