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- Question 1 of 7
##### 1. Question

In a group of 60 people, 27 like mexican food and 42 like indian food and each person likes at least one of the two cuisines. How many like both the cuisines?

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted. - Question 2 of 7
##### 2. Question

Which functions satisfy $latex f(A\cap B)=f(A)\cap f(B)$ for any two sets $latex A$ and $latex B$?

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted. - Question 3 of 7
##### 3. Question

Given any set $latex A$, find an injective map from $latex A$ to $late A\times A$.

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted. - Question 4 of 7
##### 4. Question

In a competition, a school awarded medals in different categories. 36 medals in dance, 12 medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons and only 4 persons got medals in all the three categories, how many received medals in exactly two of these categories?

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted. - Question 5 of 7
##### 5. Question

Given any set $latex S$, find a surjection $latex S\times S\to S$.

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted. - Question 6 of 7
##### 6. Question

Suppose there exists a strict injection (i.e. that is not a surjection) from $latex A$ to $latex B$. Can there also exist a bijection between $latex A$ and $latex B$?

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted. - Question 7 of 7
##### 7. Question

Find a function $latex f:A\to A$ which is not identity but $latex f\circ f=Id$.

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Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.