At a certain university 523 of the seniors are history majors or math majors(or both).There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history?

chillywilly12a
2020-12-16
Answered

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Nola Robson

Answered 2020-12-17
Author has **94** answers

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

1)

Inclusion-Exclusion Formula:

If A and B are any two finite sets, then$\left|A\cup B\right|=\left|A\right|+\left|B\right|-\left|A\cap B\right|$ .

Let H, M be the sets of seniors whose major is History and Math respectively.

It is given that 523 seniors are history majors or math majors or both.

Thus,$\left|H\cup M\right|=523$ .

It is given that 100 seniors are math majors.

Thus,$\left|M\right|=100$ .

The number of seniors majoring in math and history are 33.

Thus,$\left|H\cap M\right|=33$ .

Step 2

Evaluate the number of seniors majoring in History using Inclusion-Exclusion principle as follows.

$\left|H\cup M\right|=\left|H\right|+\left|M\right|-\left|H\cap M\right|$

$523=\left|H\right|+100-33$

$523=\left|H\right|+67$

$\left|H\right|=523-67$

$\left|H\right|=456$

Therefore, the number of seniors majoring in History is 456.

1)

Inclusion-Exclusion Formula:

If A and B are any two finite sets, then

Let H, M be the sets of seniors whose major is History and Math respectively.

It is given that 523 seniors are history majors or math majors or both.

Thus,

It is given that 100 seniors are math majors.

Thus,

The number of seniors majoring in math and history are 33.

Thus,

Step 2

Evaluate the number of seniors majoring in History using Inclusion-Exclusion principle as follows.

Therefore, the number of seniors majoring in History is 456.

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Where f is a function. Prove that this difference is an uncountable set.

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Start from the vertex x and change the ${i}^{th}$ bit to 1 and then change all bits gradually one by one moving leftward from $i-1$ to 1 to n and back to i.

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My work: We define a xy-path ${P}_{i}$ as follows:

Start from the vertex x and change the ${i}^{th}$ bit to 1 and then change all bits gradually one by one moving leftward from $i-1$ to 1 to n and back to i.

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