Describe each of the following sets by listing its elements: a) {x|x elementof N

Question

Describe each of the following sets by listing its elements: a) {x|x elementof N and x^2 - 5x + 6 = 0} b) {x|x elementof R and x^2 = 7} c) {x|x is one of the year Dallas Cowboys won the super bowl.} Find ((S) for the set S = {a, b} Which of the following candidates are binary or unary operations on the given sets? For those that are not, where do they fail? a) x compositefunction y = greatest common multiple of x and y; S = N b) x compositefunction y = x + y; S = the set of Fibonacci numbers. c) x# = the string that is the reverse of x; S = the set of all finite-length strings of symbols from the set {p, q, r} d) x compositefunction y = x + y; S = R - Q

Explanation / Answer

Problem 12.
a. {x|x in N and x^2 - 5x + 6 = 0}
x^2 - 5x + 6 = =
==> (x - 3)(x - 2) = 0
==> x - 3 = 0, and x - 2 = 0.
==> x = 3, x = 2.
Therefore, the set is: {2, 3}.

b. {x|x in R and x^2 = 7}
x^2 = 7
x = +/- sqrt(7)
==> x = +/- 2.6458
==> x = 2.6458, -2.6458.
Therefore, the set is: {-2.6468, 2.6458}.

c. {x|x is one of the year Dallas Cowboys won the super bowl}
This is so generic to arrive at an equation, anyways the answer is:
{1972, 1978, 1993, 1994, 1996}

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