SETS 1 (Exercise 1.1 to 1.3)

The collection of good hockey players of India

• Set

• Not a Set

The collection of Prime numbers

• Set

• Not a Set

Which of the following is a null set?

• A = {x : x is a natural number and 4 < x < 5}

• B = {x : x is even prime number}

• $C\ =\ \left\{x\ :\ x^2=25,\ x\ is\ an\ odd\ integer\right\}$

• D = {x : x is positive multiple of 3 less than 6}

Which of the following is infinite set?

• Set of letters of the English alphabet.

• $\left\{x:\ x\in N,\ x<100\right\}$

• $\left\{x:\ x\in R,\ 1<x<2\right\}$

• $\left\{x\ :\ x\ \in Z,\ x^2=36\right\}$

The set of natural numbers which divide 42 is

• {1, 2, 3}

• {1, 2, 3, 6, 7, 14, 21}

• {1, 2, 3, 6, 7, 14, 21, 42}

• {42}

The set {3, 6, 9, 12, ...} in the set-builder form is

• {x : x is a multiple of 6}

• $\left\{x\ :\ x=3n,\ where\ n\ \in N\right\}$

• $\left\{x\ :\ x=3n,\ where\ n\in N\ and\ 1<x<4\right\}$

• $\left\{x\ :\ x=3n,\ where\ n\in N\ and\ 1\le n\le4\right\}$

A set which does not contain any element, is called

• empty set

• infinite set

• power set

• none of these

If every element of A is also an element of B, then

• A is the subset of B

• B is the subset of A

• A is not the subset of B

• None of these

 $IfA\subset B\ and\ A\ne B,\ then$  

• A is called a proper subset of B

• A is called a super set of B

• A is not a subset of B

• B is a subset of A

The set of real numbers $\left\{x\ :\ a<x<b\right\}$ is called  

• semi-closed interval

• closed interval 

• semi-open interval

• open interval