Solution to Solve the following two " union " type questions: (a) How many bit strings of … - Sikademy
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Solve the following two " union " type questions: (a) How many bit strings of length 8 either begin with 2 0s or end with 1 1s? (inclusive or) (b) Every student in a discrete math class is either a computer science or a mathematics major or is a joint major in these two subjects. How many students are in the class if there are 36 computer science majors (including joint majors), 29 math majors (including joint majors) and 5 joint majors?

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a) Let set A be the bit strings of length 8 beginning with two 0s:

|A|=1\cdot1\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2=2^6=64

Let set B be the bit strings of length 8 ending with one 1s:

|B|=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot1=2^7=128

Let C be the bit strings of length 8 beginning with two 0s and ending with one 1s:

|C|=|A\cap B|=1\cdot1\cdot2\cdot2\cdot2\cdot2\cdot2\cdot1=2^5=32

Then

|A\cup B|=|A| + |B|-|A\cap B|=64+128-32=160


b) Let A be computer science majors

|A|=36

Let set B be math majors

|B|=29

And joint majors are |A \cap B|= 5

Therefore there are students in the class:

|A \cup B|=|A|+|B|-|A \cap B|=36+29-5=60


Answer:

a) 160

b) 60

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Question ID: mtid-5-stid-8-sqid-3630-qpid-2329