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Prove that the Poset has a unique least element
Prove that if (A, <) has a least element, then (A,≤) has a unique least element.
Ans: Let (A, ≤) be a poset. Suppose the poset A has two least elements x and y. Since x is the least element, it implies that x ≤ y. Using the same argument, we can say that y ≤ x, since y is supposed to be another least element of the same poset. ≤ is an anti-symmetric relation, so x ≤ y and y ≤ x ⇒ x = y. Thus, there is at most one least element in any poset.
Prove that Prim's algorithm produces a minimum spanning tree of a connected weighted graph. Ans: Suppose G be a connected, weighted graph. At each iteration of Prim's algorithm
1.)3 3/8 divided by 4 7/8 plus 3 2.)4 1/2 minus 3/4 divided by 2 3/8
There is a staircase as shown in figure connecting points A and B. Measurements of steps are marked in the figure. Find the straight distance between A and B. (Ans:10) A ns
statement of gauss thm
sinX/cscX+secX/cosX=1
write 107 in expanded form.
2cos^2x-sinx=1......Find x
0.34/100
If a school has lockers with 50 numbers on each combination lock, how many possible combinations using three numbers are there.
I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?
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