Are the Following Pairs of Sets Equal? Are the Following Pairs of Sets Equal? Question Answer (i) \[ A=\{2,3\} \] \[ B=\{x:x \text{ is a solution of }x^2+5x+6=0\} \] \[ x^2+5x+6=0 \] \[ (x+2)(x+3)=0 \] \[ x=-2,-3 \] Therefore, \[ B=\{-2,-3\} \] Since \[ A=\{2,3\}\ne\{-2,-3\}, \] the sets are not equal. (ii) \[ A=\{x:x \text{ […]

Pair the Equivalent Sets Pair the Equivalent Sets Set Number of Elements \[ A=\{1,2,3\} \] 3 \[ B=\{t,p,q,r,s\} \] 5 \[ C=\{\alpha,\beta,\gamma\} \] 3 \[ D=\{a,e,i,o,u\} \] 5 Conclusion Equivalent sets have the same number of elements. Since \[ n(A)=n(C)=3, \] therefore \[ A \sim C \] Also, \[ n(B)=n(D)=5, \] therefore \[ B \sim

Are the Following Sets Equal? Are the Following Sets Equal? Set Roster Form \[ A=\{x:x \text{ is a letter in the word “reap”}\} \] \[ A=\{r,e,a,p\} \] \[ B=\{x:x \text{ is a letter in the word “paper”}\} \] \[ B=\{p,a,e,r\} \] \[ C=\{x:x \text{ is a letter in the word “rope”}\} \] \[ C=\{r,o,p,e\} \]

Which of the Following Sets are Equal? Which of the Following Sets are Equal? Set Elements (i) \[ A=\{1,2,3\} \] \[ \{1,2,3\} \] (ii) \[ B=\{x\in R:x^2-2x+1=0\} \] \[ x^2-2x+1=0 \] \[ (x-1)^2=0 \] \[ B=\{1\} \] (iii) \[ C=\{1,2,2,3\} \] \[ \{1,2,3\} \] (iv) \[ D=\{x\in R:x^3-6x^2+11x-6=0\} \] \[ (x-1)(x-2)(x-3)=0 \] \[ D=\{1,2,3\} \]

Finite and Infinite Sets Finite and Infinite Sets Set Finite / Infinite Reason (i) Set of concentric circles in a plane Infinite Set Infinitely many concentric circles can be drawn. (ii) Set of letters of the English alphabets Finite Set There are only \[ 26 \] letters. (iii) \[ \{x\in N:x>5\} \] Infinite Set Natural

Examples of Empty Set Examples of Empty Set Set Empty Set or Not Reason (i) Set of all even natural numbers divisible by 5 Not an Empty Set Numbers like \[ 10,20,30,\ldots \] satisfy the condition. (ii) Set of all even prime numbers Not an Empty Set \[ 2 \] is an even prime number.

Write the Set in Set-Builder Form Write the Set in Set-Builder Form Write the set \[ \left\{ \frac12, \frac25, \frac3{10}, \frac4{17}, \frac5{26}, \frac6{37}, \frac7{50} \right\} \] in set-builder form. Solution Observe the pattern: \[ \frac12=\frac1{1^2+1} \] \[ \frac25=\frac2{2^2+1} \] \[ \frac3{10}=\frac3{3^2+1} \] Therefore, the general term is \[ \frac{n}{n^2+1} \] Hence, the set-builder form is

Set of All Positive Integers Whose Cube is Odd Set of All Positive Integers Whose Cube is Odd Write the set of all positive integers whose cube is odd. Solution The cube of an odd integer is always odd. Therefore, the required set is the set of all positive odd integers. \[ \{1,3,5,7,9,11,\ldots\} \] In

Set of All Vowels in the English Alphabet Which Precede q Set of All Vowels in the English Alphabet Which Precede q Write the set of all vowels in the English alphabet which precede q. Solution The vowels in the English alphabet are \[ a,e,i,o,u \] The vowels which come before \[ q \] are

Match the Sets in Roster Form with Set Builder Form Match the Sets in Roster Form with Set Builder Form Roster Form Matching Set Builder Form (i) \[ \{A,P,L,E\} \] (vi) \[ \{x:x \text{ is a letter of the word “APPLE”}\} \] (ii) \[ \{5,-5\} \] (v) \[ \{x:x^2-25=0\} \] (iii) \[ \{0\} \] (i)