AMU MCA Sets And Relations Previous Year Questions (PYQs) – Page 1 of 2

An investigator interviewed $100$ students to determine the performance of three drinks milk, coffee and tea. The investigator reported that $10$ students take all three drinks milk, coffee and tea; $20$ students take milk and coffee, $30$ students take coffee and tea, $25$ students take milk and tea, $12$ students take milk only, $5$ students take coffee only and $8$ students take tea only. Then the number of students who did not take any of the three drinks is

Let $Y={1,2,3,4,5},; A={1,2},; B={3,4,5}$ and $\phi$ denotes null set. If $(A \times B)$ denotes cartesian product of the sets $A$ and $B$, then $(Y \times A)\cap (Y \times B)$ is

Let $A={2,3,4,5,\ldots,16,17,18}$. Let $\approx$ be the equivalence relation on $A \times A$ cartesian product of $A$ and $A$, defined by $(a,b)\approx(c,d)$ if $ad=bc$, then the number of ordered pairs of the equivalence class of $(3,2)$ is

Let * be a binary operation on the set $R$ of real numbers defined by $ a * b = \frac{3ab}{7} $, then the identity element in $R$ for $'*'$ is

Let $R$ and $S$ be any two equivalence relations on a set $X$. Then which of the following is incorrect statement

Consider the following relations in the real numbers $R_1={(x,y)\mid x^2+y^2\leq25}$ $R_2={(x,y)\mid y\geq\frac{4x^2}{9}}$ then the range of $R_1\cap R_2$ is

If $A$ and $B$ are disjoint sets, then $B\cap A'$ where $A'$ is complement of $A$ is equal to

Which of the following is an incorrect statement?

For any three sets $A, B$ and $C$ the set $(A \cup B \cup C)\cap (A \cap B' \cap C')' \cap C'$ is equal to

Let $P={\theta;\ \sin\theta - \cos\theta = \sqrt{2}\cos\theta}$ and $Q={\theta;\ \sin\theta + \cos\theta = \sqrt{2}\sin\theta}$ be two sets. Then,