Query 3

course Mth 151

6/6 8

Open Query 3:*********************************************

Question: `qQuery 2.3.15 This might differ from the problem as given in the text, but you should be able to answer it for the given sets: universal set U = {a,b, c,…,g}, X={a,c,e,g}, Y = {a,b,c}, Z = {b, ..., f}

What is the set (Y ^ Z')U X?

Your Solution

We start off by doing (Y^Z’). First you do Z’ which is a set of elements not in Z that is in the Universal set. So Z’= {a,g} then you find what is common between Y and Z’ and you reach the set {a} after this you find the union between this and set X which is {a,c,e,g}.

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Question: `qGive the intersection of the two sets Y and Z'

Your Solution

So if you find Z’ which is what is in the Universal set that is not in set Z then you get {a,g} but the only common element to Y is {a} so {a} is the intersection.

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Question: `qQuery 2.3.32 (formerly 2.3.30). This was not assigned, but you answered a series of similar questions and should be able to give a reasonable answer to this one: Describe in words (A ^ B' ) U (B ^ A')

Your solution:

(A ^ B’) is the elements in A that are not in B and the elements in B that are not in A

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Question: `q2.3.53 (formerly 2.3.51) Is it always or not always true that n(A U B) = n(A)+n(B)? This was not among the assigned questions but having completed the assignment you should be able to answer this.

Your solution:

It is not always true because the statement reads (A U B) is the sum of A and B which is not true because there may be elements in common it would only be true if set a and b have nothing in common

okay

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Question: `qQuery 2.3.60 X = {1,3,5}, Y = {1,2,3}. Find (X ^ Y)' and X' U Y'.

Your solution:

(X ^ Y) ' = {1,3}' = {2, 4, 5} and X’ U Y’ would be {2, 4, 5}

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Question: `q2.3.72 A = {3,6,9,12}, B = {6,8}.

Your solution:

AxB and BxA

AxB= {3,6) (3,8) (6,6) (6,8) (9,6) (9,8) (12,6) (12,8)}

BxA= {(6,3),(6,6),(6,9),(6,12),(8,3),(8,6),(8,9),(8,12)}

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Question: `q2.3.84 Shade A U B

Your solution:

You would shade everything in A and B and everything outside it would not be

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Question: `qQuery 2.3.100 Shade (A' ^ B) ^ C

Your solution:

You would shade what is common between B and C but not including A

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Question: `qQuery 2.3.108. Describe the shading of the set (A ^ B)' U C.

Your solution:

Everything outside A and B not in common with C but C would be shaded because of the union involved

Explain a the diagram better

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Question: `q2.3.114 Largest area of A shaded (sets A,B,C). Write a description using A, B, C, subset, union, intersection symbols, ', - for the shaded region.

Your solution:

(C’^B’)^A

Ok because order doesn’t matter

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Due to a carelessly typed password, a block of files failed to post correctly on 6/7/10. This file might have been among them, and is being posted on 6/8/10, a day late.