Subject Experts Solutions for Chapter: Set Theory, Exercise 1: PRACTICE EXERCISE

Consider the following

$\mathrm{I}.$ $A\cup \left(B\cap C\right)=\left(A\cap B\right)\cup \left(A\cap C\right)$
$\mathrm{II}.$ $A\cap \left(B\cup C\right)=\left(A\cup B\right)\cap \left(A\cup C\right)$

Which of the above statement(s) is/are correct?

In a group of $50$ people, two tests were conducted, one for diabetes and one for blood pressure. $30$ people were diagnosed with diabetes and $40$ people were diagnosed with high blood pressure. What is the minimum number of people who were having diabetes and high blood pressure?

In a class of $60$ students, $45$ students like music, $50$ students like dancing, $5$ students like neither, then the number of students in the class who like both music and dancing is

Let $A=\left\{1,2,3,4,5,6,7,8,9,10\right\}$, then the number of subsets of $A$ containing exactly two elements is

If $A=\{x: x$ is a multiple of $3\}$ and $B=\{x: x$ is a multiple of $4\}$ and $C=\{x: x$ is a multiple of $12\}$, then which one of the following is a null set?

If $A=\left\{x\in R: x^2+6x-7<0\right\}$ and $B=\left\{x\in R: x^2+9x+14>0\right\}$, then which of the following is/are correct?

$\mathrm{I}.$$\left(A\cap B\right)=\left(-2,1\right)$                $\mathrm{II}.$ $\left(A\backslash B\right)=\left(-7,-2\right)$

Select the correct answer using the code given below 

$A, B, C$ and $D$ are four sets such that $A\cap B=C\cap D=\mathrm{\varphi }$. Consider the following

$\mathrm{I}.$ $A\cup C$ and $B\cup D$ are always disjoint

$\mathrm{II}.$ $A\cap C$ and $B\cap D$ are always disjoint

Which of the above statement(s) is / are correct?

What is the number of natural numbers less than or equal to $1000$ which are neither divisible by $10$ nor $15$ nor $25$?