Problem 2.4 Compute the cardinality of the following sets. You may use other tex

Question

Problem 2.4 Compute the cardinality of the following sets. You may use other texts or the internet. (i) Two digit positive odd integers. (ii) Elements present in a sucrose molecule. (iii) Isotopes of hydrogen that are not radioactive. (iv) Planets orbiting the same star as the planet you are standing on that have moons. Assume that Pluto is a minor planet. (v) Elements with seven electrons in their valence shell. Remember that Ununoctium was discovered in 2002 so be sure to use a relatively recent reference. (vi) Subsets of S = {a, b, c, d} with cardinality 2. (vii) Prime numbers whose base-ten digits sum to ten. Be careful, some have three digits.

Explanation / Answer

(i) Two digit positive odd integers - This set goes from 11,13,15,...,95,97,99. The number can be found out as

n = (99 - 11 / 2) + 1 = 45

Cardinality = 45

(ii) The chemical formula of Sucrose is C12H22O11

It has 3 elements - C, H and O.

Cardinality = 3

(iii) The three most stable isotopes of hydrogen: protium (A = 1), deuterium (A = 2), and tritium (A = 3).

Of which, tritium is radioactive.

So, non radio active isotopes of Hydrogen are 2.

Cardinality = 2

(iv) Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto have moons.

Cardinality = 7

(v) Elements in Group 17 having 7 electrons in their valence shell - F, Cl, Br, I, At, Ts, Lu, Lr.

Cardinality = 8

(vi) The number of subsets with cardinality 2 of S = {a,b,c,d}

(a,b) (b,c) (c,d) (a,d) (b,c) (c,d)

Cardinality = 6

(vii) 19, 37, 73, 109, 127, 163, 181, 271, 307, 523, 541, 613, 631, 811

Cardinality = 14

Cheers!

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