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38)
Let π΄ = {2,3,4,5,6,7,8,9} and define an order relation βΌ on π΄ by the following: For all π, π β π΄, π βΌ
π if, and only if, there exists an integer π‘ such that π = π‘π. Then, in the poset (π΄, βΌ)
A) The minimal elements are 2 and 3 and the maximal elements are 6, 8 and 9.
B) The minimal elements are 2, 3, 4 and 5 and the maximal elements are 6, 7, 8 and 9.
C) There are no minimal elements, nor any maximal elements.
D) The minimal elements are 2, 3, 5 and 7 and the maximal elements are 5, 6, 7, 8 and 9.
39)
Let π΄, π΅, πΆ and π· be sets, and let π β π΄ Γ π΅, π β π΅ Γ πΆ and π β πΆ Γ π· be relations. Then the
relations (π β π) β π and π β (π β π), from π΄ to π·
A) must not be equal.
B) are sometimes equal, and sometimes not, depending on the sets π΄, π΅, πΆ,π· and the relations π , π
and π.
C) must be equal.
D) are not defined
In a Hasse diagram of a poset (π΄, β€), a pair of distinct elements π and π of π΄ are connected by a line
segment if, and only if,
A) either π β€ π and there is no π β π΄ such that π β€ π β€ π, or else π β€ π and there is no π β π΄ such
that π β€ π β€ π.
B) either π β€ π or else π β€ π.
C) π β° π and π β° π.
D) π β€ π.
Much appreciate!
1.Β Β Β Β Β Β A woman launches a boat from one shore of a straight river and wants to land at the point directly on the opposite shore. If the speed of the boat (relative to the water) is 10 mi/h and the river is flowing east at the rate of 5 mi/h, in what direction should she head the boat in order to arrive at the desired landing point?
The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5 defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01, and 0.005, respectively. Find the mean of the probability distribution.
(3a-5)(9a2+25)(3a+5)
Suppose three test kits are tested at random. Let D represent the defective test kit and let N represent the non-defective test kit. If we let X be the tendon variable for the number of defective test kits, construct the probability distribution of the random variable X
Let G be a finite group.let S={gβ¬G|g^5=e}, where e is identity element of G.show that |S| is odd.
4) Express the negations of each of these statements so that all negation symbols
immediately precede predicates.
a) Rita will move to Oregon or Washington.
b) if it rains today then the home team wins.
c) βxβyP(x, y) β§ βxβyQ(x, y).
d) βxβy(Q(x, y) β Q(y, x)).
1.Β Β Β The weight of Group 1:Jay - 43 kg, Stella - 42 kg, Tilly - 44 kg, Joanna - 53 kg. Consider samples of size 3 that can be drawn from this population.
a.Β Β Β How many possible samples can be drawn?
b.Β Β Β List all the possible samples and the corresponding means. Β
c.Β Β Β Β Construct the sampling distribution of the sample means.Β
Suppose a, b, c, d have proper positions 1, 2, 3, 4 respectively, i.e., the cor-
rect sequence (from position 1 to 4) is a, b, c, d. Write down all the deranged
sequences. What is the combinatorial expression for their count?
#339914 on Dec 2023