Sets — Class 12 Mathematics PYQs

Consider the following statements :

I. The set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is an infinite set.

II. The set of all odd integers less than $1000$ is a finite set.

Which of the statements given above is/are correct?

For any three non-empty sets $A,B,C$, what is
$(A\cup B)-\{(A-B)\cup (B-A)\cup (A\cap B)\}$
equal to?

The Cartesian product $A\times A$ has $16$ elements among which are $(0,2)$ and $(1,3)$. Which of the following statements is/are correct ?

1. It is possible to determine set $A$.
2. $A\times A$ contains the element $(3,2)$.

Select the correct answer using the code given below :

Consider the following statements :

1. $A=(A\cup B)\cup (A-B)$
2. $A\cup (B-A)=(A\cup B)$
3. $B=(A\cup B)-(A-B)$

Which of the statements given above are correct ?

Consider the following statements :

1.	The set of all irrational numbers between $\sqrt{2}$ and $\sqrt{5}$ is an infinite set.
2.	The set of all odd integers less than $100$ is a finite set.

Which of the statements given above is/are correct ?

Consider the following :

1.	$A\cap B=A\cap C\Rightarrow B=C$
2.	$A\cup B=A\cup C\Rightarrow B=C$

Which of the above is/are correct ?

If $A=\{\{1,2,3\}\}$, then how many elements are there in the power set of $A$ ?

Consider all the subsets of the set $A=\{1,2,3,4\}$. How many of them are supersets of the set $\{4\}$ ?

Consider the following statements in respect of two non-empty sets $A$ and $B$ :

1. $x\notin (A\cup B)⟹x\notin A$ or $x\notin B$
2. $x\notin (A\cap B)⟹x\notin A$ and $x\notin B$

Which of the above statements is/are correct ?

Consider the following statements in respect of two non-empty sets $A$ and $B$ :

1. $A\cup B=A\cap B$ iff $A=B$
2. $A\Delta B=\varphi$ iff $A=B$

Which of the above statements is/are correct ?