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3. Prove or give a counterexample to the following: For a set A and
binary relation R on A, if R is reflexive and symmetric, then R must
be transitive as well.
binary relation R on A, if R is reflexive and symmetric, then R must
be transitive as well.
DISCRETE STRUCTURES
1. Prove the following formulas for all positive integers n.
a) 1 + 2 + 3 + 4 + 5 +...+ n = n(n + 1) :2
b) 1 + 4 + 9 + 16 + 25 + ...+ n2 = n(n + 1)(2n + 1) :6
c) 22n - 1 is a multiple of 3
1. Prove the following formulas for all positive integers n.
a) 1 + 2 + 3 + 4 + 5 +...+ n = n(n + 1) :2
b) 1 + 4 + 9 + 16 + 25 + ...+ n2 = n(n + 1)(2n + 1) :6
c) 22n - 1 is a multiple of 3
Find the number that is 3/4 of the way from 2/5 to 4 2/3.
Write in polar form, draw a picture, show steps.
-12R + 5U
I have looked everywhere in my text book and can’t find a thing like this
-12R + 5U
I have looked everywhere in my text book and can’t find a thing like this
A pair of dice is thrown. If the sum on the two dice is 9, find the probability that one of the dice showed 3.
Find domain and range of (answers should be subsets of R):
f(x)= 3/(2x -1)
f(x)= 3/(2x -1)
Find domain and range of (answers should be subsets of R):
f(x)= x/(x^2+1)
f(x)= x/(x^2+1)
Find domain and range of (answers should be subsets of R):
f(x)= 1/(5x-6)
f(x)= 1/(5x-6)
Find domain and range of (answers should be subsets of R):
f(x)= 3/2x -1
f(x)= 3/2x -1
an inclined ramp rises 4 meters over a horizontal distance of 9 meters. How long is the ramp
